Saudi Arabia is under US influence and that's not going to change. Saudi Arabia is the biggest buyer of US weapons and has US military bases and the US is never going to give up Saudi Arabia. China shouldn't keep distance with Iran for the sake of Saudi Arabia.Theses countries have economies that are relatively easy for China to "uplift" since they mostly have problems which china has largely solved. Their use is more from being over-weighted on a military front, vs China, which is underweighted in military but over-weighted in economy. They help buy china time to preserve access to resources and providing ready consumer/industrial markets while at the same time China can buttress them by being a backstop against economic sanctions. The middle east element is most difficult because picking up Iran probably also involves the most trade-offs compared to turkey or pakistan. If at least a few of GCC states could remain neutral (i.e. Qatar or Dubai) it would help since picking up Iran will antagonize Saudi Arabia.
I believe China should no longer just be indifferent to ouside world and choose a side and form an alliance with Iran, Syria, Iraq, Yemen etc in Middle East. Russia is helping Syria thwart the illegal US forces and China should too. China's neutral foreign policy loses potential allies of China and isolates China.