We kayaked Tobermory last July and found the same parking issues. We parked one day at Dunks Bay and one day at Big Tub light house (About a mile North West of the center of town) The Big Tub parking area was our favorite because of the location. You can access great paddling from this spot quicker than that of Dunks Bay. (It is also free, but now sure about overnight parking because we did not do any overnight trips)
Each place has their up's and down's.
Dunks Bay is again, a bit of a paddle from everything, but it has a great sandy beach to lauch from and also a nice spot to cool off with a swim after your long paddle.
Big Tub has the great location, but you will not be lauching from a sandy beach. This location is for calmer seas. The spot to launch is a sliver of an inlet to the left of the walk-way. (About 10 ft wide, but at least 20ft deep, so you have some protection) Another plus to this location is the swimming afterward. You jump off the large rocks into crystal clear waters. Fantastic for snorkeling!
Hope this helps. I will be writting about our trip real soon. I will touch on everything. (camping, food, drinks, parking and of course paddling)