I think the insurance issue would indeed make PPL training in these aircraft a little on the pricey side, assuming cover could be obtained at all.
As you know, the SR20 does now have EASA approval and the SR22 should have soon, though unless you already have a UK IR I can't see the attraction of putting them on the G register.
As far as training in N-reg aircraft goes, the reply below is what I got from the CAA some time after asking them whether I could do my IMC training in an N-reg (an SR20 as it happens.)
I'll leave it to the reader to interpret the response; suffice it to say that I ended up doing the IMC in various Cessnas and Pipers in the end, all distinguished by having a 'G' painted on the side.
Anyway, over to the CAA:
IMC TRAINING IN A U.S. REGISTERED AIRCRAFT IN THE U.K.
The country of registration of the aircraft in which the instruction is given is not in itself significant.
Because you are contemplating the use of a U.S. registered aircraft, it will be necessary for you to ensure that the instruction is carried out in compliance with the relevant regulations of both the U.K. and the U.S.A. You should seek advice from the relevant U.S. authority, in this case the Federal Aviation Administration (FAA), as to which specific U.S. regulations bear upon the proposed activity and what needs to be done to comply with them.
I am unable to advise you on what the scope of these regulations might be but there are at least two questions which immediately come to mind.
Is the aircraft to be used appropriately certificated for the giving of instrument flying instruction under U.S. regulations as well as being suitably fitted for the intended purpose (in your case with dual controls and an instrument / radio navigation equipment installation on a scale which will allow the instructor to cover all aspects of the IMC course) and will the instructor and Flight Examiner be appropriately licensed or permitted under U.S. regulations to give the instrument flying instruction and conduct the flight test?
You will appreciate that the instructor must be capable of giving a course of instruction to a U.K. CAA recognised IMC syllabus. If permission to conduct the training has to be given to a U.K. licensed instructor, he would be obliged to comply with any conditions stipulated by the U.S. authorities in addition to acting within the privileges of his U.K. licence and Instructor Rating.
The requirement to be licensed or hold an appropriate permission under U.S. regulations would apply to the CAA Authorised Examiner as well if the U.S. registered aircraft is used for the IMC test.
I must also point out that if valuable consideration is given or promised in respect of the training or the test, it will constitute aerial work under U.K. law and consequently permission will have to be sought from the Secretary of State for it to go ahead in accordance with the provisions of Article 115 of the A.N.O. In addition to this you will need to find out if there are any U.S. rules governing commercial activity conducted in a U.S. registered aircraft which need to be observed.
Queries about U.S. regulations should be addressed to the Federal Aviation Administration.