You can add a FI rating to your JAA licence either by doing a FI course in the UK or in some parts of the US, less schools there than there were. There may not be much chance of using it in the US but you'll have it for return to the UK.
The FAA system is entirely different and as far as I know you will need a FAA CPL/IR before you can add a CFI rating. May be an opportunity to gain another qualification, people are always looking for BFRs in the UK.
While you're doing it: Keep off the bottle old son!