How do I get my cat to quit disrupting our sleep?

Another cat question!

My cat seems to have the most energy around 1–4 in the morning. This is particularly awful because my boyfriend gets up around 4:30 for work so those are his last hours of sleep and lately we have both been up every 10 minutes during that time. My cat during the day is affectionate and a snuggler but not anywhere NEAR how much attention he wants at those hours of the night. He walks all over us (literally and figuratively, ha), sits on our heads, licks our hair, meows, purrs in our faces….pretty much anything he can do to keep us awake and giving him attention. Sometimes I try to snuggle him against my body and pet him so he just calms down and goes to sleep but it doesn’t really work. He also seems to have restless leg syndrome at night, he never stays still.

Anyhow, WHAT DO I DO? It’s more of a problem for my boyfriend, but it’s also an annoyance to me, and I therefore spend that time of night awake trying to get the cat off of my boyfriend so he can sleep, and therefore I am left to deal with the cat.

I don’t want to put him outside our room and close the door because then he meows and will be lonely. And my point of adopting a cat is to not make him lonely anymore! I just want to teach him that it is fine to sleep and snuggle with us at night, but meowing and butt-in-the-face at 3 am is not okay. How? Help?