Dunno if that would work. Adobe (unlike Amazon) would require your credit card billing address to be in the US. Not sure if it has changed now, but a few years back i tried buying Adobe Lightroom from the US site and was unable to do so.

My workaround was to buy the retail box from Amazon, ship it to a friend in the US and have them email the license key to me.

It would still be breaking the terms of the license agreement. Presumably that'd be just as bad as getting a bootleg copy.

You need a US credit card that can be address-verified.

Are you allowed to do that? Or to put it another way, if you got raided by the BSA, would they have a problem with that?

how would they differentiate from someone like me, who has software bought in the US, while living in the US, but who now lives in the UK?

I imagine it's pretty easy to find out if someone has been living in the US within the past N month or not.