I think the secret on making reasonable larger-caliber RACs is just to ignore the previously-established conventions on autocannon calibers.
You can BS some reasoning about how the moment of inertia of the barrel cluster grows too non-linearly to make very large caliber RACs viable or some other plausible-sounding techno-babble...
more or less what I did here.
Once you've established that 10 is too high, it's really open season.
Most autocannons do 100 points of damage per ton of ammo, but that's not a hard and fast rule as the -2 class ACs have been doing 90 damage/ton of ammo for literally no reason at all and TPTB have never seen fit to retcon this odd (but irritating) incongruity.
A RAC-4 can have 25 shots per ton and hit exactly 100, a RAC-6 can have 16 and hit 96, a RAC-7 can have 14 and hit 98, a RAC-8 with 12 shots/ton hits 96, and a RAC-9 with 11 shots/ton hits 99. SRM-6s, AC-2s and several sizes of MML do a worse job of rounding than this so I don't want to hear any complaints about my math here.
On top of that, RACs can't use special ammo so there's no need to worry about coming up with new modifiers for the AP rounds or any other weird rules hitches.
The problem with a RAC-10 is that it's very difficult to differentiate it from an UAC-20. Previously-established conventions would mean that a RAC-10 is in the neighborhood of size and weight for an UAC-20, and the average expected damage of the 5 shot bursts is a little higher than the UAC-20 on double-tap. The UAC has bigger hits but fewer of them, the RAC either outranges it and looks holistically better or ends up as a weird gimmick.
I'm not sure why your LAC/10 only reaches to 9 hexes; it feels over-tuned. You do realize that autocannons suck, right? You can make pretty much any canon design better by swapping the AC/10 for a PPC and heat sinks and that's
without DHS. You don't need to worry about putting in compromises to avoid making a LAC/10 obsolete the vanilla AC/10; the vanilla AC/10 has sucked since day 1 and any weapon worth taking will obsolete it. 12 hex maximum range is quite reasonable. Hell, you could sneakily give it the same 15 hex max range and make it just a better AC/10 and you're not going to be turning the game on its head or anything.