Ok then, "self discharging" disconnect at around 40% means that your BMS is working fantastic, better than most. I am surprised that the epropulsion people didn't tell you as much.
Lithium batteries will completely not work again if you drain them down to zero volts. It is recommended to store lithium batteries long term at around 50%. So having a BMS that disconnects at around 40% could very well be a battery saver. To store them over the winter you need to charge them a little every month or get a programable charger that you can set to turn on at 45% and turn off at 50%. Since batteries "wear out" more on the top and bottom of the charge, this "middle charging" will have the least degrading effect on the batteries.
This is especially helpful with a battery that only has 500 cycles. This tells me that it is not a LFP (LiFePO4) battery but some kind of Lithium, maybe LMC (Lithium Manganese Cobalt), because the lowest cycle count I have ever seen on a LFP was 1000.
It being something like a LMC battery tells me that it is most likely a 12S battery when they call it a 48V and will need a 50.4V charger for a 12S lithium battery.
The GrenePower 51.2V, 32Ah LiFePO4 that I found on amazon is a LFP battery and will need a 58.4V charger for a 16S LFP battery. If you have a programable charger then you can charge either one of them to whatever you want.
Being that weight is your primary concern, your best bet might be to stick with the Greenpower 32Ah.
The Greenpower looks like it uses the cylindrical cells in a 16S, 8P configuration. Couple reasons I don't like cylindrical cells is there is a lot of empty space between them, so they are less power dense for their size. Another is that for every P more than 1, the battery is that many more times likely to fail, for example an 8P battery is 7 times more likely to fail than a 1P battery. I don't know of any LFP batteries that small that don't use the cylindrical cells. I think all the LFP batteries that are less than 100Ah use them.
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