There's a reason why SAMs feature larger diameters than their A2A counterparts. Could this be due to requiring that much more fuel volume to overcome altitude difference while preserving range and flight characteristics especially wrt steering post boost? Seems the sans booster SM-6 is a better SAM to convert for A2A as it appears more in line with typical thinner AAM diameters and length to width proportions. My guess is an AAM being fired at around mach 1 and at altitude means it can slim its frame down and lose that extra fuel to maximise speed and reduce drag vs a long range SAM requiring that extra volume. It a long range SAM kept the same proportions, it may be an issue wrt acceleration stresses on the frame during boost. Also seems to require considerably more boost to overcome inertia. So on balance, we have this convergence where medium to long/ultra-long ranged AAMs are usually thinner and longer in proportion compared to long range SAMs. Been true since the HAWK and Guideline. AAMs converted to SAMs though ... plenty of examples of those, usually medium ranged AAMs and ends up being point defense SAMs. Business case issue perhaps.
Unlike HQ-9 the air to air version appears to be a single stage missile whereas both HQ-9 and SM-6 ship launched are two stage missiles iirc.
The HQ-9 makes use of thrust vectoring and the SM-6 uses fins. Nearly 7m for HQ-9 full length. Compare their diameters. No PLAAF/PLANAF fighter in current service is going to be carrying a HQ-9 under a wing. I suppose that's why PL-17 and P-21 are the ULRAAMs. I've no doubt the "ballistic", rocket only missile will not have the HQ-9's diameter. Converting a HQ-16/Buk to A2A? R-37M sort of resembles that but not quite. Still a completely different missile. The Americans just saved a tonne of money and time to field a ULRAAM with the SM-6. Good for them but in the past they would have developed a ground up latest and greatest new AAM. Maybe the AIM-260 is where the resources have gone. A2A SM-6 is admittedly what I'd have done a long time ago. It's really one of the few SAMs that can be suitably converted to an AAM.
Oh another reason SAMs have larger diameter is to house a heavier warhead. Yet another optimisation issue wrt conversions.