I have a sideways answer that might not be satisfying: instead of playing D&D, play a RPG that uses cards, e.g. the https://en.wikipedia.org/wiki/Castle_Falkenstein_(role-playing_game) system, or something similar. I understand that playing cards are generally permitted as long as you are neither removing them from the deck to cast them away nor gambling. Generating characters on some other day of the week would be necessary.

I don't know what's required to observe the sabbath, but I think that all or most of the gmless games by Ben Robbins could work: https://www.lamemage.com/

For Microscope you would want some cards with the light and dark markers filled in to place the timeline with, and for Follow you would want the ability to cast lots, but that could be adapted if it's a problem. Of those games, Follow and Kingdom are the most similar to D&D. The only change to the rules is that when it says to write something down, you just wouldn't, but words spoken take priority anyway.

There is a new game called In This World that just ended a Kickstarter, I've played that one on a camp with new players, and we could have done that with spoken words alone.