I ran a tikka action in a KRG X-Ray chassis for many years in PRS competitions. Their actions are very smooth, and their barrels are very accurate. I never competed with the tikka barrel, but i'm sure it would do just fine. The most you'll be shooting typically on a stage is 12 rounds, and most stages are less (8-10 rounds), so I think you'll be ok on barrel heat. And i've also run a XLR chassis quite a bit, and like them alot.

The trend these days seems to be heavy rigs that produce almost no recoil, and most people compete with a 6mm variant, but 6.5 always works well (and easier to spot impacts at the long distance targets). I don't have any experience with the Havoc HIT, but i'd probably lean towards getting the chassis that you like, and building up from there.