Maybe factor in a new stem, as 22.2-31.8 shims can be hard to find.
Loads of nice BMX stems around though.
Most Mtb moto style bars are 22.2mm (7/8″) – Surly, Stooge, etc.
Though the Stooge aluminium Moto bar is normal 31.8.
You can of course fit proper Moto bars – Renthal and Protaper make nice ones. You even get a cool retro crossbrace pad with them 😎
I’ve not tried cheap steel Moto bars from eBay (seen them for £15 or so) but I’m not sure how well they’d stand up to full on MTB abuse. Would he fine for pootling around though I imagine.