Why should a vendor check your licence before selling the MH? Would you expect them to inspect everyone's licences!Downsizing and getting it re-registered is possibly going to be subject to the same admin delays.
Just an idea, probably of no interest, but do you have a friend with a C1 who could drive it to a campsite for you so you could at least get some use, otherwise I fear it's going to be a long, long time.
Personally I think it is disgraceful for a vendor not to check you can actually use the vehicle before taking your money - any reputable salesman knows the score.