When I was on uberman (for about a week before I got a nasty cold and then overslept) my naps were typically about evenly distributed between RLD (rem/light/deep). Except my noon nap, which is almost always almost entirely REM (15mins+). In fact, I seem to have REMnaps at noon even if I've been monophasic then get a short night's sleep and then take a noon nap.
When I was on everyman this summer, some of my naps would be like you describe, but as I said, noon was almost always great, and I'd fairly often get 10-15mins REM in my other naps.
Puredoxyk recommends tweaking schedules with tiny shifts. If that's possible for you logistically, then I recommend sliding your naps around, maybe 15 mins earlier. Try a new time for 5 days or so, and see how that affects your tiredness and the REM. Then try another shift. Keep logs about what works/doesn't. I haven't actually done this myself, so I'm curious how this works for you.
What do your cores look like, zeo-wise? If you're not getting a lot of deep at night (around 1.5h+ I'd say) then it totally makes sense that your body would want more during the day.
(also, are you using the main zeo histogram or going into the menu on the left? it gives you stuff quantized by minute, which is much more powerful, and can sometimes elicit that what looked like mostly REM and light actually had some deep, or whatever).