Lead acids have a range of about 10.5V - 15V.
Charged: ~90.0V
Discharged: ~60.8V
So if you went with 18650 cells, your figured would be:
22s: 70.4 - 90.2V
If you go with 11.1V - 14.5V instead, then it would be:
Charged: ~87.0V
Discharged: ~66.6V
18650's would then be:
21s: 67.2V - 86.1V
Btw, I'm going with a voltage range per cell of 3.2V - 4.1V to get the a boost in cell longevity. You can go to 3.2 - 4.0V, but then you'd need 22s (70.4 - 88.0V) but also gain even more life. However, this starts lifting the bottom voltage up to high. You "can" go down to 2.8V with most cells, but you won't get much capacity from 3.2 to 2.8 and the drop off is pretty quick.
And, the common nomenclature here for battery design is series first, then parallel. So, 21s10p, for example. A 10p21s would mean you need 21 bms units, and I doubt that's what you mean
I mention this because perhaps on other forums they put it the other way around. Here it's known to be series/parallel, and others reading may get confused later on (or perhaps yourself reading others threads).
21s20p is 400 cells. That's a lot for a pack. So yes, I would agree on the 20p range and not the 50p or so as a single build. They still need to be accessible and removable fairly easily if need be.
Use 3 parallel packs of 21s20p, and then use balancing connections to hook them all together. This will allow 1 bms to handle the whole lot. It's gonna be a mess of wires, though, unfortunately.
2 main wires pos/neg
22 balance wires connecting each pack together
The balance wires only need to handle a few amps, maybe <10A as balancing shouldn't draw a lot of power, especially if the cells are good and well balanced when building the packs.
Ultimately, I'd suggest to go with high power cells, like those used in power tools.
What's the kWh ratings of the electric motor(s)? If they are 1kWh running at 72V (nominal), then you're looking at close to 14A. With 50p, 14A shared across those would be 0.28A per cell. This is well within most cells capabilities. The high voltage makes this doable.
Replacing the charger would probably be a good idea, unless you can program it to function with different charge settings.