We are hiring a car the second week; I've been looking at a one-way rental from Leeds back to Heathrow for that week. But I see your point and will check out just getting the car for two weeks... it seems wrong somehow to pay for one to just sit in a boatyard for a week, but it may well be the easiest and most economical overall.
Thanks to you and the other folks who've suggested alternate airports. I already bought tickets to Heathrow -- got the airfare squared away before we started looking at other aspects of the holiday. Live and learn!!! We're coming the end of March, so I hope stoppages won't be an issue.
Me again --
Thanks to everybody for the great suggestions, and helping me crack the code of the train, coach, and bus fares. (How did anyone ever do this before the internet?)
Now it looks like we have plenty of choices -- I'm looking principally at Canal Boat Escapes or Rose Narrowboats on the L&L, or Chas Hardern near Chester, though the Reading/Thames idea is interesting too...