So I've finally made the move from from SS modelling amps to a tube amp (Blackstar ht5) and my tone is much nicer. However when I play high gain solos I still feel something is lacking, the tone isnt as warm as I'd like it, its a bit weak and thin

I have an Epi LP Custom. Would installing better pickups in it help get the most out of my amp?
Installing new pickups may help slightly but you probably won't get the thick high-gain solo tones you're looking for. Buckethead's rig consists of high-gain amps such as Mesas - pickups alone won't get you the tone you want.

You could try a Tubescreamer-type pedal (Ibanez TS, Maxon OD, Digitech Bad Monkey) to boost your tone and give you a little extra body/sustain.

While we're at it... what EQ settings are you using?
Ibanez RGA121 | ESP LTD H-1000
Axe-FX Standard
the epiphone pickups sound muddy so getting better ones would help you get the most out of your guitar and amp
Yh, I'm not a fan of the epi pickups, the neck pup sounds thin and the bridge sounds muddy.
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It would try getting a boost pedal first. Take a look at an Ibanez tubescreamer.