Arrowhead,
GinSlinger has pretty much nailed it for you.
Delta Connection (ex-Comair) have a few Senecas (I think they are Seneca II's). They are the only JAA school operating them - and even they have a big bunch (about 20) Seminoles that they usually use for training.
Having said that - one way round it (in theory) would be to do the rating on the easiest and cheapest aircraft and then do a conversion course to Seneca when you understand what is happening (the Oxford, Tyler, Seneca of which you speak is a Seneca III - with turbochargers and overboost problems that you don't need for those INITIAL six to ten hours of training).
The other problem is that if your FAA SEP licence was issued "on the basis of" your JAA licence then the answer may be "No - you cannot add another rating to it". Problem there is that, despite the official paperwork and guidance, individual offices (and officers) have their own take on the regulations and, especially if you FAA was issued before the regs changed in July 2002, some will allow you to add, some will not.
A slightly deeper problem is that if you do a JAA MEP class rating you then need to apply for the rating (mailing log book and licence and application form [with a cheque for £64] to the CAA in Gatwick) before you can have it added to any FAA qualifications - and that, in turn, will require the standard £15 to the CAA and application forms to both the CAA and FAA (as you do now for all licence exchange).
This would mean that you are now grounded - as you would have no JAA licence to support the FAA one that you carry.
If you really want to do it in Florida - then why not do an FAA rating (which is slightly harder anyway) - and then convert THAT into a JAA one??
Having said that - you will still (VERY likely) need to carry a safety pilot until you have some 25 to 50 hours of MEP experience. The "logging" of flight time would come down to the integrity of the flight instructor (who will almost definately want to log it P1 himself)...............and YES, you would almost certainly have to pay for the instructor to ride with you during this time.
Why don't they call you back?? Some are just generally crap at it - others may not have the interest to respond if they cannot give you the training that you are demanding - others have muppets on the phone who don't have a clue what they are talking about if it is not straight forward, standard PPL, training for the average Joe.
I would also look at the finances a bit closer - with the FULL cost of travel to the USA (full costs of full day for visa application - including travel to the Embassy, driving to Gatwick or wherever for the trans-atlantic flight, the cost of living in USA [food, entertainment and transport], maybe a uniform for the school, possibly another FAA medical, extra application fees, additional instructor fees for "dual" hour building, etc. etc.) then I would not think the SAVINGS would be sufficiently significant to make it all worthwhile for the exercise you want.
Consider doing a quality course at Headcorn - which might not have landing fees for based aircraft (dunno about that??) - then consider taking an instrument rated instructor/safety pilot with you and go do some low cost I/R training before you attend the real I/R course. Get the check list from the school that you will go to for the I/R and see if the local school will accept that check list for operations in their own aircraft. Overall - a much better product.
Send me an "e" if there are any other questions nagging at you.