A bit of Google-fu has led me to a brand called Dr. Bob's that is unflavored but still contains fluoride. I haven't tried it, so I can't attest to it, but it looks promising.
I have non-24-like symptoms, so I have absolutely no schedule where I can just say "I'll do it at 8 p.m. every night", because depending on where I am on my cycle, I could be long asleep by then. The solution to this for me is literally just doing it before I go to sleep, whatever time that is, whether it's 4 a.m. or 2 p.m.
If pain/sensory issues are a problem, exploring small, soft-bristled brushes and different flavors might be a good idea. Children's toothpaste often comes in flavors like bubblegum that I've found are much gentler than mint, which can be harsh, smelly, and sting more if you have any cuts, swelling or other issues going on in your mouth. They also make flavorless toothpaste.
I use Dr. Bob's flavorless toothpaste and it works well for me!
There are plenty of places you can get unflavored toothpaste or tooth powder:
https://www.cleure.com/products/toothpaste-original-without-flavor
https://smile.amazon.com/Dr-Bob-Unflavored-Toothpaste-Artificial/dp/B0963WCPZC
There's unflavored toothpaste.
Are you rinsing after you spit? After brushing my teeth and tongue, I take a swig of water, swish it around, and spit it out. I rinse as many times as I need to for my mouth to feel free of toothpaste. Some people will tell you to leave the toothpaste in for the flouride, but I personally think that's nasty.
I also floss nightly, and use a dental pick and scaler like twice a week. For what it's worth, I've never had a cavity.
If you're struggling to just do the actual toothbrushing, you can try practicing mindfulness. I've learned to frequently ask myself, "What do I need right now? What do I do to address that need?" -- especially when I'm stuck on what to do or if I need to snap out of hyperfixation. Usually the answer's pretty obvious, e.g. "My teeth need to be brushed to prevent all the bacteria I collected during the day from growing new colonies in my mouth overnight. I'm going to get up, go to the sink, and brush my teeth to make sure that doesn't happen."