If you could find these (Valtain) wheels, they work. https://www.facebook.com/jetmotorsmini/videos/for-sale-12000001995-olde-english-white-jdm-rhd-4-speed-manual-with-ac-fuel-inje/278240306698150

ClassicMinisJapan do come across them here and there, if you're interested. They aren't easy to come by. And when they're available, they're not cheap. Here's a post of when they had them last. https://www.facebook.com/ClassicMinisJapan/posts/3505953446169645/  David is a good guy to talk to over there. Knows his stuff and where to come across some rare goodies. Japan Mini owners really love their small wheels. They're more into the 10's than any other sizes. They have options over there that aren't available here. Case in point with the Valtains. So I'd say they'd know for sure what would work. They're diehards for 10" wheels. Scroll through their FB page and you'll see some options. Or better yet, ask David which ones would fit the 8.4" brakes.
They also offer some newer wheels that came out not too long ago from Bon Racing. Not sure if they'd work. You can see those on ClassicMinisJapan FB and website, or on Bon Racing's site...,available in 10" and 12". 

Other than that, I'd say your options are severely limited. I went with 7.9". That may be your next best bet other than going with a custom wheel. There's a few choices of shops in the UK that make custom wheels for the Mini. If money is no object, it can be done. Depends on how bad you want 8.4" brakes.

These are some of the UK custom wheel makers that you can chat with to see what can work with 8.4s: 

https://www.specialist-components.co.uk/index.php/catalogsearch/result/?q=wheel

//www.force-racing.co.uk/wheels/

https://www.imagewheels.co.uk/#

And then there's JBW. https://www.johnbrownwheels.com/wheels/classic-mini  You could ask them if any of their offerings have that capacity/ability. I went with their 6x10 MiniLights.

Happy hunting. If you come across something that works from either of these options, or somewhere else, please post your findings, so as to help others that may want the same.

I'd like to increase my stopping ability, over the 7.9s that I have, being that I did the Vtec swap. But I've put enough money into this Mini already. Buying custom or rare wheels from out of country and larger brakes would make things spiral out of control cost wise, more so than I have already gone with this thing. So I'm dialing it back and working with what I have.

Hey Alex. My neighbor used them on his golf cart years ago. Wish I had them now.

Have you still got the 100+ alloys you got from me in '09 ?

Ive ordered the kit to swap from 8.4 back to 7.5. Thanks

...fit 7.5" brakes.

Basically nothing fits over an 8.4" disk & caliper, though there used to be a few ghastly creations that were offset far enough to clear - with the obvious disasterous effects on handling, ride, and the suspension components and you needed Sportpack or Miglia arches to cover them.
There are a few 7.9" kits around, but in all honesty you're better off sticking to 7½" S brakes.

Wanting to fit 10" wheels to a mini with 8.4" disks. Anyone know what my options are?