From what I heard GarageFive is the most experienced with the H22. But that was years ago so other shops such as Speed Syndicate might know by now.
I had a 5speed swap done at G5 and I sourced my own parts and just paid for their labour which was about 1000 dollars if i remember correctly. Again this was many years ago but you should be able find more info on VPC and it'll give you a general idea of how much you might be looking at.
Other than that just call around and ask.
Good Luck
Cheers,
Mike