If its a licence being issued on the basis of your current UK/JAA PPL then you'll be doing a BFR - no need for TSA or visa. Go to the FSDO for the paperwork, then to the flying school for the BFR groundschool and check ride.
Ok, just re-read your message...
As its a full FAA-PPL you're after then I think you will need the visa as its probably still considered an initial licence...
On the TSA clearance front, speak with the TSA - it may be possible to get the clearance moved to another facility? (IO-540 or SoCal might have a better idea on this). You have to remember that not everyone flight trains on an M1 visa - for instance if you are working in the US on a H1 (or H4 as a dependent) then that also covers you for educational courses, but you still need the TSA clearance. The one thing you cannot do though is train after entry into the US on the VWP.