Maybe just a fitting for a shaft would work? I upgraded the shaft in my TSR 2 driver and TSi3 fairway but also bought a GT 2 fairway to fill a distance gap.

Off the rack - probably not. Always the possibility that a new shaft in the GT through a fitting may be noticeable.

If your TSR is still filling the hole in your bag, then a GT will only have a small improvement. If your are having dispersion issues or not getting enough launch for consistent distance, then a GT may give you more consistency. Do note that a live fitting may suggest a GT-2 is a better improvement. You just need to decide if a GT model is a want, or, a need.