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F T/R Competition Barrel Contour

I shoot a medium palma in F open (a 6XC) - it's not a dedicated open rifle though, and would go heavier were I to build one. But not because of heat - just for the extra weight. Weight helps control recoil, which helps you stay on target, which helps you shoot fast, which helps you with the wind which is most of your score. I imagine the same holds true for TR. Get as much barrel as the rules allow.
 
I'm betting you will be able to make weight with a heavy palma barrel. I have a Barnard action, which is considered heavy by some, with a 34" heavy palma and I make weight.

If you weigh everything you have, including rings, bases, etc., you can use a barrel weight calculator to determine what will work and keep you under the limit. Lilja has one on their site that is accurate to less than an ounce. You can also take measurements on your current barrel to determine its weight if it is already on your action. This is will allow you to figure out how heavy you can go. I would figure in a 4-6 ounce leeway in for scale variations.