I don't think a 20ft sailboat is suitable for the number of people and supplies you mention.
IMO You'll push the boat WAY below it's lines unless it's a heavy displacement
boat, it's not going to be a safe ride.
If size is a true limiting factor then go with a heavy displacement
boat so it can hold everything safely and stay reasonable on it's lines. Look at some of the George buehler designs.
The 18ft Mary Read is a open day sailor, you could stretch it out to 20 or 21 ft without any I'll effects.
Or a boat designed almost exactly what you are looking for is the 25ft Little Big Man, - trailerable heavy displacement boat which has a short cabin
, and enough inside bunking for 2 people and a cockpit
for another two in sleeping bags. It has a galley
, but you could convert the galley
into another bunk instead, but it might be nice to have a galley if the weather
goes sour and you just want some warmth and hot food
. It also has a toilet. Going ashore to take care of your business is fine in rural coast line, but if you have to go quick for whatever reason, then a head
Anyway just some thoughts for you.