Jim,
First off welcome.
Second I believe you. 1977 was the big year GM decided to start putting Buick engines in Oldsmobiles, Oldsmobile engines in Pontiacs, Pontiacs in Buicks and Oldsmobiles, and Chevy engines in all of them. It's my understanding a lot of law suits against purists went against GM that year.
Third, interesting, as I would think a 3 on the tree in a 77 passenger car would be quite rare...in fact, in 77 I'm surprised a manual was even offered in a luxury car like a Cutlass. I know the base model GM and Ford trucks still had them and a few low buck GM cars had them.
Now....as to your question....
If you wanted to drop in an intercooled V6, you really have your work cut out for you. You'd need a donor engine, donor intercooler...plus possibly having to fab it up to make it work....donor ECM, donor wiring....and you'd have to convert to an electric fuel pump.
A hot air V6 would probably be the same, minus the intercooler...
A "before black" V6 from '78-'83 would probably be even easier....would bump your 110 hp up to 160-180 hp.
But in any case also factor in you'd need to redo your exhaust.
Also not sure if your 3 speed manual would stand up to much abuse. I don't think GM built them very tough because they were designed to work with a 100 hp/190 tq engine. I could be wrong, but I know GM really started cheaping out in the durability department in the mid 70's.
Another thing....I'm going to guess your car probably already has the stout 8.5 rear...I'm not sure if any of the '77 A bodies came with anything different...but if it has the 7.5 rear (you'd have to consult a collondade A body expert on this), you'll want to change it too.
Of course the cheaper alternative to more power without a lot of work is to drop in a 455 engine. If you still wanted to keep it a standard and didn't mind some work, you might be able to install a Muncie 4 speed. Again not sure as most of these cars were automatics, but a 455 is definitley doable...just that 3 speed probably won't live long behind it.