Wheelchair-friendliness is a problem. Because Lake Union varies in depth about 2 feet annually (controlled by the Corps of Engineers via the locks) many Lake docks are on fixed pilings and simply compensate with steps or not at all; few have long ramps like you do on saltwater. My marina is very pet friendly, but the finger piers are so narrow I would never risk a wheelchair on them, and the pier gates would be a daily pain in the butt.
Find out the true length and beam of the houseboat you're smitten with, and start haunting Craigslist for slips. I have not seen a brokered or privately offered slip that did not also appear on Craigslist.
Are you looking for a short-term lease, or purchase, or seasonal occupancy ?