One bass, standard tuning. One Bass VI tune B-B. One Bass VI tuned F-F, capoed to F# so he has an open B on the second string. Piano player doubling bass parts with his left hand a lot of the time. And a bass clarinet in the horn section.
I'm pretty sure this is Mike League's Big Bottom. That arrangement had to start out as an inside joke. It works, but it's ridiculous.
You've got better sources than mine. The liner notes on Family Dinner call it as two baritones and electric bass.
And you're right about it working while still being ridiculous. In lesser hands it would have been like trying to eat a sticky bun made entirely out of cinnamon.

