Congrats on your first specialty pistol.
It is impossible to free float the barrel on a TC but you can install aluminum pillars in your stock and or you can buy some forends that use polymers or aluminum to get you the best possible accuracy set-up.
Also, there is one unique rest set-up that is quite different, called the Bower rest System Bower Shooting Products LLC
You would need a forend from them and have a wood grip also modified, plus the rest itself. For LR steel shooting or pd's this would be my favored choice.
For hunting circumstances Neal Cooper sells a forend that I would buy for regular hunting (with or without a bi-pod).