Any boat purchase requires concessions and flexibility.
Can you change your budget?...maybe. Can you change your requirements, easier, and maybe.
Almost every trawler will have 2 "cabins", so the question becomes what other sleeping space is available. A friend of mine has spend considerable time on a traditionally rigged tall ship, and is quite comfortable with his allotted space of a 6'X3.5' berth, with the same amount of storage underneath, that's in a shared space with 30 other berths.
He can happily spend a month on the couch with no complaints.
So if the budget is fixed, maybe re-evaluate your cabin/sleeping requirements? Many boats in the $100k range will sleep 6 or more...just depends on how flexible everyone is.
Bottom line?...if everyone wants to do it bad enough, you'll find a way.