Summit North in the C&D Canal -- Bear, Delaware -- probably can meet some of your requirements. They have a long face dock
that might work with your beam. Call first. Not much else around there in the immediate vicinity, though.
The marina in Delaware City is up an older, now unused part of the Canal, not sure you'd have room to turn in there. Nice folks, but not much of a town for a long period of time. Worth a call, maybe.
Might be something in Lewes, but that'd take some research
. We've only stayed at the city dock, which is quite nice, but I don't think they can make that a long-term answer.
The State-run marina in Indian River Inlet is very nice, but I don't remember much in the way of service
facilities... and it's not within walking distance to towns. Bicycles could work...
Don't know first-hand about other DE options, but you could check ActiveCaptain if you haven't already.
The haul-out issue is likely the biggest deal. Thought I saw a thread on here somewhere about hauling a beamy cat somewhere around Annapolis
... i.e., not Delaware...