I have hunted with T/Cs since they came out. I too was very dis-satisfied with not achieving my desired accuracy.
Anything used to cushion or float the barrel away from the forend was at best a temporary fix. I live in Alaska so when freeze up hits the POI changes. When it thaws and starts raining it changes again.
I have only this one photo left but one can get the idea by looking at the machined perch in the barrel channels. This black material is extremely hard so no aluminum piller is required.
Tony Gettel at tony'sforendsandstocks.com machines these perches in his T/C wood stocks and then puts an aluminum piller in as a regular process.
I made the stocks pictured and to date I do not own a hunting handgun that shoots over 1 inch at 300 yards. Year to year I take my short barrel 338 out every 3 months and fire one shot at a target. This summer just before the August first deer season I shot that one shot and had to adjust windage two clicks. First time in a number of years.