Carlton plays a 335, I think that's a hard sound to duplicate on a strat...as far as amps....I read an article about the Kid Charlemagne solo and Larry said he played his 335 through a cranked late 60s BF Fender Princeton Reverb.....he said he mainly used fenders back then, but he also played some boogies too...probably the Mark I.....these days he uses Dumble amps...
...I personally think a TS9 wouldn't be a good match for what you're looking for...you probably want a smoother OD.... I think Fretfire has been trying to achieve a similiar tone and is waiting on a Zendrive...I for one I'm curious on how it'll perform....