Anyone know for sure, one way or the other, if the parking restriction at Y&BC also extends to Boardwalk? I agree that parking at the Boardwalk makes the most sense, unless there's a restriction there as well, one the OP didn't think to check before asking us our opinion(s). And it would be unfortunate if the idea we think makes the most sense, doesn't, because of something we didn't know.
If for some reason the Boardwalk is also restricted during that time, then you could park in the Swan & Dolphin lot, but there is a parking fee. You could also park in the Studios and walk or boat to the Y&BC, but if you weren't planning to go to a park that day, again, you're paying for parking just to eat at Beaches & Cream.
ARE you planning to go to a park that day? If so, were you planning on going back to your resort for a rest that day? Because were I in your shoes - staying offsite, wishing to eat at Beaches & Cream but can't park at the Y&BC (and possibly not at Boardwalk), I'd just anticipate going to the Studios that day, even more than Epcot. When it feels like lunch time, leave your car in the Studios lot and walk or boat to Y&BC. have lunch at Beaches & Cream, soak up the resort atmosphere, pool hop (JOKING!), and then go back to the Studios when you're rested. If you're going to park-hop at all that day, make it to the WS section of Epcot, so it'll be reasonably easy to get back to your car in the Studios lot.