Could the reason why PLAN wants UVLS to be hot-launch capable is that HJ-18 couldn't fit into H/AJK-16?
Because the rest of PLAN VLS missiles are either small enough to fit into H/AJK-16 (HHQ-16, CN VL-ASROC) if they're hot-launched or gigantic poles of explosives that are cold-launched (aka HHQ-9).
I'd guess if they could start over, they'll enlarge H/AJK-16 and integrate HJ-18 into it. UVLS will be a Hot/Cold-launched VLS instead of a hybrid (my guess is cold because as you said, exhaust gas management in VLS for large missiles is a pain).
TL;DR. Chinese version of K-VLS & K-VLS 2
I think it's better to view the UVLS as a ground up, future proof VLS system rather than just seeing it in relation to YJ-18 as if it is the primary weapons system for the UVLS.
If they went for a H/AJK-16 or Mk-41 style VLS arrangement and they still wanted to have a large diameter like 850mm to accommodate cold launched large diameter weapons that can't be managed by a hot launch vent, well you'll end up being more space inefficient for launching those sorts of weapons than the UVLS.
Everything is a trade-off.
And no, we don't have any evidence to believe HQ-9 could fit in the H/AJK-16 VLS.
YJ-18 definitely cannot fit in the H/AJK-16 VLS.
We never had any indication that they intended those weapons to be fit in the H/AJK-16 VLS to begin with.
The H/AJK-16 VLS is not very flexible, because it can only carry Yu-8 and HHQ-16 that we know of.
The UVLS we know can launch YJ-18, HHQ-9, new dual stage ABM, new ASBM/HGV, and likely a number of other missiles in development given that the UVLS is newer and the standard VLS for the PLANs high end combatants and given it is also much larger and more flexible than H/AJK-16.
That's why I see H/AJK-16 VLS as more of a dead end and more limited than UVLS. It's just far less future proof.
Tbh I'm surprised you would see the UVLS as space inefficient -- personally I see it as quite an elegant solution for being able to accommodate large diameter weapons while also being able to hot launch weapons if they choose so for individual cells, without needing the extra space needed for a dedicated common venting system.
It means each individual cell had the option to be cold or hot launch as one sees fit.