Sorry this answer is so late - I mainly watch the island forums.
I live just north of Lewes and call New Rd. my home port. From about the time of your post, the traffic between here and New Rd. has been insane. It's been like a never ending holiday weekend! I have turned around I think 5 times during this period when heading there.
I occasionally launch out of the ramp at Roosevelt inlet. However, I have two mirage drives plus a Torqeedo Travel 1003. I rarely use the motor, but I always use it when I launch at Roosevelt. It would be a hard row in a boat that rowed well to get in/out against the tide so I doubt it's a good place for a cat.
There is a small state owned unimproved launch at 38.690859° -75.136715° on the west side of Rehoboth Bay. You can get to that spot by just crossing Rt 1, not driving south on it. It looks like it may be a touch muddy at low tide but is only a few miles away so you may want to check it out.
Edit: Here's a link - click on the little yellow man in the thumbnail and it will open up a large picture: https://maps.google.com/maps?q=38.690859%C2%B0+-75.136715%C2%B0