We have three cats (right now, have always had between 1-4) and I feel your pain about the nighttime yowling. We have one guy right now that is a serious pain in the ass and we did the whole vet thing and ended up with a behaviorist who came to the house and assessed him and gave us some strategies. Here is what's worked for us.
Shut the cat out of the bedrooms at night and get an air purifier and/or noise machine. It may get worse before it gets better as it sings the song of its people right outside your door the first few nights. Our screamer still patrols yowling but it is MUCH less than when we used to let him into our room.
Is your cat microchipped? If so, get a microchip feeder and put enough food in at night so that you know hunger isn't one of the factors contributing to the screaming. Have DS top it off if needed in the am, but best if there is just enough there until you want to be up and around.
Get some new, interactive toys and play with the cat for 10-15 minutes before bedtime. This helped the most with the yowling by our loud guy and the other two love it a lot. Look for the ones on a string that are feathers that flutter or the small insect ones or neon worm ones (you soft of safety pin them onto the stick/string) are our cats favorites. Housecats are often bored and having playtime one to two times a day helps a lot with any anxiety stemming from that. I got all of ours on Amazon. THEY LOVE THEM way more than the little mice and toys that we can just toss or leave around on the floor for them to play with.
Do you give the cat catnip? Get some and give it a little pinch at night after play time. Some cats can take it or leave it, but our yowler loves it and it seems to mellow him out right before bed. He rolls all around in it and then blisses out. He'll return to the spot we put it and roll around over and over and we just sweep it up in the morning if there's any left.
Finally, add a high perch or two to your home. This also soothes our loud/nervous guy. I was skeptical this would help but it really has. He likes to be up high observing and he goes there to sleep too.
Also - lots of cats will eat cardboard - they love it and if they are just gnawing on the edges of boxes it isn't going to hurt them. I'm not sure it warrants prozac without any other contributing factors?