Although I know very little about the B2B, this sort of problem does happen from time to time. My experience has been that generally the CAA are fairly flexible. JAR FCL allows them to give anyone suitable a temporary TRE authorisation. So it is possible to go to the USA or wherever and get checked out/tested by someone who is fairly obviously equivalent to a TRE in the other country.
The probem these days, of course, is that this needs to be repeated for LPCs. It therefore makes sense if the person who goes and gets the special "test" will or can be authorised as a TRE in the UK subsequently.
Don't forget to try other JAR FCL countries for an existing B2B TRE.