supply out of sink with demand? Is that even possible?

So I'm new to the bf boards here so excuse me if I get the lingo wrong

This is my third time breastfeeding, but I'm totally confused. I have a circadian rhythem disorder called Delayed sleep-phase syndrome (DSPS) that pushes back my hormone, sleep and body heat cycles by several hours. Partially due to this I stay up until about 4 AM and sleep until noon (DH and I both work from home so we both get enough sleep). I nurse on one side only at each feeding...it was what worked best the first two times so I just started doing it this time.

Newbie baby is almost 3 weeks old and nurses about every two hours during the day. While I'm sleeping I SOAK the bed, but when I get up he continues to nurse every 2 hours and drains me dry (no leaking between feeds). Towards evening (maybe starting at 10pm) he starts reducing the time between feeds until he is just constantly rooting...like he'll go an hour and a half, then half an hour, then constant switching. During this time I feel TOTALLY empty on both sides and he is constantly upset.

Around 2am he falls asleep for the night, and may get up at 4 or may go longer, like 6 am (when DH transfers him from the cosleeper for me since I'm sleeping). I usually have to feed from both boobs at this feeding and still feel empty. DH brings him to me almost every two hours like clockwork after that, and AGAIN I am sloshing in giant milk puddles each time I roll over while constantly rotating my blanket to get away from the wet part. This whole cycle repeats daily.

What the heck is going on? Is the cluster nursing he does at night draining me, or is he cluster nursing because my supply is lower at that time and he's not getting enough from the one boob? Shouldn't things have regulated a bit at this point? I feel like I don't have enough in the evenings and I have WAY too much in the mornings (when I am sleeping, if that makes sense). Is this related to the wonky sleep schedule? Things were so totally chaotic life-wise with the first two that I don't remember this being an issue (we had NO schedule and my sleep was heavily regulated with medications back then). Any suggestions?