My TS-808 is a glorified Standby switch...

[GibsonGM]

Yes, you probably hit the nail on the head, Ian.  Most of the noise in there is HF.  You could try a 'better' opamp (not sure what you're using, but they make lower noise versions like TL072), but that's not "to spec" for a TS.  A quick fix might be to place a small cap across your output jack terminals....something from 10 to 500pF (experiment).   How much noise you get also will have to do with how much you have the gain up...how the wires run to the pots in the box, grounding scheme, power supply filtering, etc.  That's a science in itself!
Glad you got it working!

[jrc4558]

Since you are not usingthe exact same taper of the tone potentiometer, the noise doesn't rise gradually as you boos treble frequencies, but rather "kicks in" at the extreme rotation. Noise will be there no matter what you do though. Its just how much of it can you actually live with.
If you want a smoother control - why not use a 10kA wired backwards instead of a linear 25k? Sonnically - not much diff, but much better control, albeit in reverse...