Fluke 37 seems indeed to be a good contender. It need very little power and has a lot of space. The problem is availability and that 2,000 counts are about as low as you can get. I'm thinking along two different lines. A) a somewhat universal solution that anyone can cram into just any low power bench DMM or B) a solution for a affordable bench meter that is still in production and/or have high availability (such as warehouses full of NOS) that can be some sort of "standard DMM" in this context.
I hope that Fluke take note and do a updated low cost, low power battery DMM. But on the other hand, what fun is that? This is a electronics forum and the whole point is sometimes to build something yourself!
Some has suggested to build a 3D-printed case around a hand held, and that's certainly a possibility but not everyone has a 3D printer or a printer with sufficient space (mine can print max 12x12cm, in practice 11x11cm) and since the market is saturated with handhelds, we probably never can reach a consensus of which meter to use. One thing that would help is a meter with a ribbon or flex cable to the LCD, but that is probably very unusual today.
I must find my old Beckmann, as its very reminiscent of Fluke 37, but not identical. I think it is this one:
https://www.desmoines-classifieds.com/Madison-County-/Household-Goods-/Beckman-360-digital-multimeter-with-leads-as-is.SHTML Only 2,000 counts but have a 20.00 ohms mode. I think it has C- or D-cells (no external power what I can remember) and run for ages and ages. But again, where is the fun in that? It doesn't need any hack to work on batteries.