I looked around on AliExpress to get an idea of the available batteries and their properties (capacity, discharge and dimensions) and they seem really good. It seems easy to get a reputable 5Ah battery and they all have high discharge currents (>10A continuous) that the BLDC motors can make use of. One of the physically largest ones I could find had a diameter of 26.8mm and a length of 65.2mm, so I'll model a D27 x 66mm cylinder.

Those discharge currents are also a bit worrying. I really don't want a short, because these batteries are capable of discharging like 70W continuously. At that capacity, I might consider going with a non-removeable setup (a 26650 with prefixed wires) but I'd still like removable ones if possible (it's one of the stretch-goal requirements).

Wouhh!! That's a first. Underpromising in this Aliexpress battery industry? The listing claims 5Ah but reviews are coming in and they're all >5.35Ah. Keep the current draw low and over the 5.5Ah boundary is possible.

Anyway, I had modelled in the battery and... wow:

It just perfectly slots in. I can't believe it. I was losing hope that a solution could exist but a path forward is right here that can still deliver on my desired requirements!