IMO,
don't replace the grille cloth. Why do you think people are paying ridiculous $$$ for Fender's "relic" guitars? People love that look, and besides... IMO again, if you do that, you're just spending $$$ to devaluate it.
I'm pretty adept when it comes to restoring, actually just cleaning, gluing, etc. Bringing back what is there, not putting something new on, so I'll share my trick for cleaning grille cloths with you.
Oven cleaner!
STOPPPPPPPP!!!!!!!!! Just kidding!!!
In all seriousness, but still at your own risk, this has worked for me in the past.
1st I have to ask... Are you single or is your significant other tolerating of strange abuses of the bathtub related to mid winter restorations of whatever? I once spent a week working on an old set of racing wheels in the tub, one at a time, on an upside down milkcrate of course to not damage or scratch the tub, I spent couple days on each one, stripping a few coats of race car paint overspray and polishing them... I would have much preferred doing that job outside, but it’s a lot more pleasant inside in mid January…
Back to the grille cloth. Put in the tub or shower, don’t get it wet yet and spray the crap out of it with 409 or similar, Simple Green might work even better but I'm not crazy about the smell. Use something that's fairly harmless, and that you like the smell of.
Grunge, old nicotine, bar grease, cat pee and whatever else will just run off of it and down the drain. Let is sit a few minutes, spray it some more til the dirt quits running out, then rinse it with some nice warm or hot water, works much better of course if you have a handheld shower wand on a hose... Actually, if you don't have that, you can't rinse it properly.
Let it drain down and dry if off as quickly as possible (pat it dry with some towels, one in each hand against the grille cloth, don’t be rough with it) so that the wood frame doesn't warp or split. You’ll have a beautifully grille cloth, and sometimes you can sort of weave the material back together around the snags with a pair of tweezers.
The reason I don't do this outside, although you could is because.... Hmmmm? I like doing it in the tub and I know something (yes I'm paranoid) isn't going to come along and steal it or destroy it while it's outside if it's left unattended and I definitely recommend rinsing with warm water and getting all of the cleaner out.
Just be ready for some derision coming from other family members who might already be questioning your sanity anyway, who knows...