I _may_ have an opportunity to pick up a compressor a bit "too large"
for my needs at reasonable cost (depends on the bidding).

GRANTED (wanna bet some people ignore this part) that doing so will
provide less air than the compressor is rated for, and GRANTED that I
don't mind that, what actual problems would be encountered by running a
5 or 10 hp compressor on a 2 or 3 hp motor AT REDUCED COMPRESSOR SPEED
(larger pulley on the compressor, or a jackshaft) such that the 2 or 3
hp motor is not being overloaded.

In engine service, lower speed is a good thing, so 3600 rpm motors wear
out much faster than 1800 rpm motors.

What, other than reduced air output that I'm willing to accept, are the
actual downsides, if any, of running a compressor slower than it's
"supposed" or rated to run?

Lack of fan action from the pulley is easily compensated by putting a
fan on it, and heat production will be lower at a lower speed anyway.

Not enough "splashing" for splash lubrication? Something less obvious I
can't think of?

While I could always harvest the large tank and try to flip the big
motor and compressor for a smaller one, the less stuff I'm trying to
swap, the better, generally.

--
Cats, coffee, chocolate...vices to live by