Well, I hate to be the one to spoil the party ... and I thought Nick might have come in here, BUT... the middle weekend, the whole island is taken up with the Manx Two Day Trial, which alternates sidecars in the north one day and the south the next and solos vice versa.
We can't ruin another bike event, so... sadly this wouldn't work. Incidentally the following weekend is the Classic Two Day, which is definitely worth a look.
Some great ideas in this thread, so I'm sure you'll come up with more.