A good heavy haul trucking company needs to be involved. As mentioned, try to find someone fairly close. I've moved several locos and cars. Cranes are EXPENSIVE. If you can do roll on and roll off it's a whole lot easier and cheaper. Biggest issue is finding a trucker with rail experience.

BUT - UP cupola cabooses are TALL. They were specifically prohibited from going through the short tunnels on the Siskiyou route because of this. If it is a short move, you might get lucky and have a high clearance route available but not likely. As mentioned by another post, cutting off the cupola might be an option. You can get the height down by picking if off its trucks (crane $$$$) but you may also need to cut off the steps and some underbody equipment (like battery box) to make it worth getting the height down. I heard of one UP caboose that moved like 55 miles on a high clearance route but had a low bridge to go under to get to its final location. I heard the movers carefully rolled it on its side because they could deal with the extra width versus height while trucking it. (Which also means a good crane crew at each end and likely a second pilot car.) Sometimes a house mover is willing and able to tackle something like this. Weight isn't the big issue buy height is. I knew one trucking company that did enough rail cars they would put on end on a homemade 5th wheel plate and the other on its own set of truck wheels where the rear rail wheels would normally go. Whatever happens, careful and complete prep ahead of time will save some bucks on everything that is hourly.

Best case scenario is going to be around $20k (rough guess) but could easily go double or triple that depending on cranes, pilot car(s), permits, extra mileage (deadhead or to a high clearance route) and fuel surcharges.

1:1 scale ain't cheap.....