So, I've been making some slight alterations to my Epiphone SG Special. So far, I've swapped the pickups (I've switched the bridge into neck position, neck into bridge position), I've switched the position of the toggle switch to where the volume knob was, and I've sanded down basically all of the gloss, so it's a really sexy looking and feeling matt finish (I'm still waiting on some finer sandpaper to finish the job).

It sounds great, and feels great.

But I'm tuning the damn thing every 10 seconds because it's a bolt-on with cheap tuners and a dodgy nut.

What's the best way to sort the tuning? I can either try and glue in the neck, then bolt it up, for some added support (the neck seems somewhat loose in the pocket). I can also obviously get some new tuners. But would new tuners help at all, when I'm certain that it's the neck pulling slightly that's getting it out of tune? I don't really want locking tuners, standard set of nice chrome Grovers is probably my option.
If the neck seems loose in the pocket fix that first. If you still have problems check friction at the bridge and nut, and if you still have problems then go with the new tuners.
Are the strings new? Do you know how to stretch and break in a new set of strings? You can tighten tuners, and blame nuts all you want, but if you don't stretch the new strings, they won't stay in tune.
Not new strings, they're a good month or so old. I ALWAYS stretch my strings when I put a new set on, or even put an old set back on.

I'll attempt to glue down the neck, possibly after installing some new inlays.
Please don't glue a bolt on neck on, thats just asking for trouble if you ever want to take it off again. Rather, get some shims and shim it up, the tighten it back down.

A month old strings aren't going to hold their tuning very well as a new set will after stretching.

Locking tuners and a good nut will defiantly help alot.
A loose neck is certainly going to make it impossible to keep in tune. This should be easily fixable without using glue.