Nipsy is driving me nuts

I always seem to have one happy cat (that would be the position
currently held by Espy - DSH) and one unhappy cat (the role filled by
Nipsy). Espy is always smiling and inquisitive and talking, but Nipsy
(16 lb long hair, possibly part Maine Coon) always seems unhappy and
scared of everything. That's ok, so I have one "curiosity killed the
cat" and one "scaredy cat".

Nipsy makes one noise, a high pitched sort of Meow. It always sounds
like a complaint but can escalate into something that sounds like he's
being tortured. Over and over. I pick him up, I play with him, I give
him food. And he starts yowling again. Ok, he is still a soft mush who
loves lying on his back with his feet spread apart so I get to rub his
tummy a lot.

The problem is that he starts yowling at around 3:45 AM. And keeps it
up. I generally feed them around 4:30 because I get up to pee and they
get excited. Sometimes I get back to sleep, sometimes I get to work
very early. I can't keep this up much longer. I need more sleep. He
just yowls every 30 seconds.

It's been going on for a year or so. There is no physical problem that
I can find, no problem peeing or anything like that. I will take him
to the vet to check on diabetes, since I had a cat that did this kind
of thing and died of diabetes. Still, he's only 3 so that isn't too
likely. He is a terrible vet patient and getting blood isn't going to
be easy. That makes a glucose test much less meaningful since it is
affected by stress.

This morning I locked him into another room for a half hour or so. No
litterbox or food or water so unless I plan on setting up something
like that it is no solution. Besides, I could hear him anyway. Just
sounding more pathetic than normal. I got to work early again today,
plus felt bad about locking him away.

Any suggestions appreciated.