I ran my XW-Pro for a full year on a single battery bank protected by one 200 amp JK-BMS. My single battery string was 360 amp hours of cells. That is still a bit below the minimum recommended by Schneider, but with 3C rated cells, they had no issue pushing out the current surges. The BMS was by far my limiting factor. I would guess that would be close to the power limit of two of your server rack batteries.
I hit the XW-Pro with all kinds of loads and never had a shut down of the BMS. The XW-Pro and XW+ use basically the same inverter board, the difference is in the control logic. So I would assume the power demand on the battery bank will be similar. At full rated power, the XW will draw about 140 amps DC at the battery bank. So yes, your 100 amp rated battery is too weak. What BMS is it using? Can you monitor it with a software app? Are you sure it is the BMS tripping and not the XW due to voltage drop? Can you adjust the BMS parameters? Does it have an overload time setting? In my JK BMS, it allows me to set a surge current value up to 350 amps, and a time delay. I have it set to allow 180 amps for up to 30 seconds. That allows for up to a 9,000 watt surge at 50 volts. It also has a Short Circuit protect setting. The default setting is 10 seconds. I don't know what current that would be, maybe the 350 amp limit of the device??
If you are able to monitor the battery, watch it close as a heavy load is turned on and see what the cell voltages do as well as the current. What error is it setting? Is it a current limit, or a low cell voltage? One weak connection between cells could cause the voltage to dip enough for a single cell low voltage error.