If it's Ford...
then it's the 370. I don't think any 345s were built with FoMoCo power plants.
The 370 WAS on the Gillig chassis. I did some research on the Gilligs when one was for sale when we were trying to decide whether we wanted to stay with the motorhomes or return to trailers, and I corresponded heavily with the owner for a short time. The 370 was an impressive motorhome, but there were so few built that I was a little concerned about chassis/drivetrain parts availability... not that it was a rational concern, mind you, and I never really researched parts availability at all.
AIR 2053 Current: 2006 Born Free 32 RQ Kodiak Chassis, & 1995 Coachmen B-van
Former Airstreams: 1953 Flying Cloud, 1957 Overlander, 1961 Bambi, 1970 Safari Special, 1978 Argosy Minuet, 1985 325 Moho, 1994 Limited 34' Two-door, 1994 B190 "B-Van"