The BMS amps size is chosen for your intended discharge to run the MW say 200 amps size to cover the 150 amps and a bit so you can leave the TV on while running the MW.
Now the charging spec says (on 200AH) you can charge at 200a if above 73F, 112a if above 41F, and 30 amps if under 41F.
You have a 100a charger and a gen to run that, so you can use that above 41F, but it is 35F and you need a recharge. Now what?
The BMS keeps the amps under its size of 200 amps, but how does it keep the 100a charger at 30 amps when the temp is below 41F?
Seems like you need a 30 amp charger