One can never give up their US citizenship without putting it in writing and passing it on two the correct people. I know of several people that have both passports and the countries ask that you use the appropriate one at each boarder. I think this website might be of use :
http://www.overthepond.info/ukguide/. Oh and about being in the country 270 days, how do they know where you stay at night? They can't even figure out the paper work for asylum seekers and instead give them permission to stay. I hope I didn't offend anyone...........
I'm not sure where you are getting you conversion done, but that seems a bit cheap. I believe the school I am at charged £1795 just for the books and £5100 for the flying including all taxes and flight examiner fees. Examiner fees cost £578 alone and that's just for two hour flight with now ground examination. Sounds like the CAA has us bent over the fence.
Good luck on converting, it seems like one of those life decisions.