If they're not on the list, there's no way you can get a UK JAR Licence.
That is incorrect. As I pointed out above, UKFT will train you for the issue of an FAA Private Certificate and then assist you complete the extra experience requirements and to pass the JAA PPL Skill Test (conducted by the owner who is, indeed, a JAA FE). This will enable you to apply to the UK CAA for the issue of a JAA PPL on the basis of the FAA Certificate in accordance with LASORS Section C. There is nothing special about UKFT in this respect, you could obtain a Private Certificate through any other flight school in the US (or, indeed, a PPL in any other ICAO contracting state) and complete the Skill Test back in the UK.
All of the talk about a 'JAR compliant' licence is rubbish - there is no such beast. This simply refers to the FAA Private Certificate which, in common with any other licence issued in accordance with ICAO Annex 1, may be validated for use within the JAA. This is currently automatic in the case of UK registered aircraft, although more stringent requirements may obtain in other European countries. A common system will be adopted throughout the EU with the implementation of Annex III to the EU Aircrew Regulation next year.