In terms of foreign policy and strategic goals:
- Non-interference in other states' internal affairs.
- Peaceful rise. In other words pushing back the China threat PR campaign.
- Avoiding full scale conflict with the US and probably any full scale conflict that might draw in the US outside of China's core interests, which is clearly identified as Taiwan and the Spratlys, less clearly so the Diaoyus/Senkakus.
- Hedging SLOC's with the Silk Road land route which requires the co-operation or non-interference of countries which may be bothered, justifiably or not, by Chinese naval "expansion", namely the US and India.
I'll refer to your four points one by one, before summarizing them:
-Non-interference: a carrier may or may not project a policy of "interference" however it will be China's actions and the way it uses its military assets that determines whether it continues to abide by its policy of non-intervention. More importantly, China has shown that it is increasingly willing to interfere to a degree or at least become involved, with the affairs of other countries, from political and economic engagement to sending peacekeeping troops across the globe, so its previous definition of non-interference is beginning to change.
-China's peaceful rise: again, China can develop a fleet of aircraft carriers while remaining peaceful. Just because it rises peacefully doesn't mean its navy has to remain without organic air support or organic fixed wing AEW. Furthermore a LHD is no more pacifist than a carrier, given its amphibious assault capabilities are as prominent as its MOOTW capabilities.
-Avoiding full scale conflict with the US: a fleet of carriers will not cause China to be drawn into conflict with the US. Just because China might have some carriers in westpac and deploy some carriers into Indian ocean doesn't mean China and the US will start fighting a hot war. What will happen is that the US and China will continue sizing each other up militarily speaking and conduct surveillance and tracking of both sides, and in that sense may result in a degree of miscalculation. But that is just as likely to occur if China had an equally large fleet of LHDs compared to carriers. There's also the fact that avoiding full scale conflict with the US requires capable conventional deterrence, in other words, the ability to fight a conventional war and either win or at least cause significant casualties to the US in event of a war, which a carrier is absolutely essential for (fixed wing AEW, CAP, strike as aforementioned)
-There are countries which will remain hostile to China which cannot likely be turned to become positive to China regardless if PLAN sailed carriers or LHDs. Poor relationships with countries are far more dependent on other factors rather than what kind of flat top are sailed. Many partner countries that China is seeking to develop its one belt one road vision with are not particularly hostile to China either, and for hostile countries that may be uncomfortable with Chinese carriers there are also a variety of other ways to mitigate their unease through political discourse and simply, say, not sailing a PLAN CSG well clear of Indian EEZ to reach waters near Africa.
What I'm reading overall from your four points is that you think Chinese carriers will be perceived by other countries as particularly aggressive and run counter to China's foreign policy positions.
My general reply is that China's foreign policy (including peaceful rise and non-intervention) can very easily remain in place while having carriers. China simply can not go around bombing random countries with their flattops or sailing too close to the coasts of nations who may be unnerved by Chinese CSGs. There are many ways to mitigate any possible unease over Chinese carriers as well, and if China didn't buy a fleet of carriers and used that money for a fleet of cruisers and LHDs it won't exactly be seen too differently by the governments of those countries.
China also should develop its military procurement based on weighing strategic needs versus strategic negative consequences, and the negative reception by other countries simply doesn't seem like a particularly significant consequence to contend to when we consider the PLAN are seeking to develop a blue water navy with significant offensive capability anyway.
There is no significant evidence that suggests a meaningful number of countries will react negatively to the existence and deployment of Chinese carriers, and that the summative effect will be detrimental to Chinese strategic goals (say, a large number of nations of the new silk road and maritime silk road, AIIB, etc leave their agreements with China).
If anything a number of those countries have no beef with China and may welcome greater PLAN ability to provide stability to SLOCs in their region of water.
A CV program that goes beyond training runs counter to all of the above. However a LHD program has a much less aggressive demeanor, is less capable offensively as you pointed out, and is much more appropriate for MOOTW such as SAR and humanitarian missions, all of which helps all of the above more, or at least doesn't hurt them as much as a CV program. That LHD's are simpler and cheaper than CV's just makes them that much more efficient to have.
An LHD is just as capable in offensive missions (amphibious assault, invasion) as a carrier, while a carrier loaded with helicopters can be just as capable as an LHD in MOOTW.
LHDs and carriers are both equally offensive minded and intended for power projection as their primary missions, while both also retain MOOTW capabilities. If some other countries do perceive carriers as being many times more aggressive then that is their problem, not China's.
LHDs are definitely simpler, smaller and cheaper than CVs however they are not more efficient at providing fixed wing AEW, strike, CAP, just as a carrier is less efficient than a LHD at delivering AAVs onto shore, sustaining a marine complement, or acting as a mother ship for LCACs.
Of course, LHDs are also far less useful in fleet vs fleet engagements as they are only able to embark helicopters (which admittedly may be useful for ASW and some degree of AEW), and lack the ability to embark long range strike fighters (for strike and CAP), and more importantly cannot embark fixed wing AEW.
If worse comes to worse and China has to fight a full scale conflict with top tier opponents beyond the First Island Chain China has no chance even if it has a few CV's which would just be juicy targets. More importantly the CV's communicate aggression rather than deterrence. Better to develop long range missiles, land based airpower, space, cyber, and even unconventional weapons which stand a better chance of actually deterring a conflict in the first place as well as being more survivable in one.
CV's are even less effective in a full scale conflict within the First Island Chain with top tier opponents, rather it ties down assets having to defend it and all of the above weapons can be both more efficient and more effective in combat than CV's.
CVs do tie down other assets that have to defend it, but it also provides significant capabilities which no other asset can provide. I've mentioned fixed wing AEW, strike, CAP already. More importantly, whether it is a high intensity war or a lower intensity operation, Chinese ships will be operating in taskgroups anyway where each ship contributes to each other's self defence, so adding a carrier into the mix does not significantly change the concept of operation for PLAN. If anything a carrier will assist the defence of the taskgroup by providing greater air defence, air surveillance and surface strike capabilities.
Whether CVs should be abandoned or even reduced in priority to better fund other weapons is another discussion, but given China is definitely seeking to project power in future beyond westpac in future, and that CVs are an essential capability in fighting against an opponent who has their own CVs (USN) as well as providing invaluable fixed wing AEW, I can't see how CVs should not be pursued.
Whether PLAN CVs will only remain sitting ducks in a full scale war against a high tech enemy is also another matter (it very much depends on when such a conflict occurs), but we've also discussed in the previous thread that there is a need to develop core carrier competencies earlier while also developing the capabilities to defend carriers. China is doing both, so unless you believe China should only develop carriers well after it has a massive fleet of escorts, capable SSNs, MPAs, and airwing ready to go I can't see any other way of reconciling its short term and medium term carrier requirements with a cautious approach in defending its carriers.
I also have no idea what you mean by "CV's communicate aggression rather than deterrence" -- the USN uses CVNs for deterring countries all the time. Aggression is very much deterrence depending on how one wields aggressive capabilities.
. Chinese planners think in terms of decades not years. Couple that with the complexities and longevity of inducting real organic air power into any navy it'll be foolish for china or any navy for that matter to start getting serious about them only when the need arises or only when it aligns with a nation's strategic interest. 