Absolutely agree with you. If it will grind, then that's got to be the choice, yes.
Wasn't meaning to suggest going further than that in Tim's case, no way - just wanted to say that I've found T&L are good for all these sorts of things, and are very sympathetic to older machinery.
In the unlucky and unlikely event that Tim's groove, coupled with any ovality, might be more than a single remaining grind can cope with, then bending the ear of people like T&L could be reassuring as they'll have a Plan B.
Also well worth getting the rods checked I reckon - for cracks first off, and for ovality of the big end eye, 'straighth' etc. Like many of us, they polish up OK on the outside . . . but it's an age thing. "When the maggot gnaws from within, then will the apple rot. . . ."
I'm always a bit of a pessimist with these things to start with, because then I can be happy if the verdict is better than 'terrible'!