I have never tested this personally so take this with a grain of salt: there is apparently a way to "trick" the controller to use the payload values for other motion groups as group 1, thus increasing the number of payload schedules available to group 1 beyond the default 10.
From what I understand, this process it long and tricky, and involved changing variables via a Controlled Start, rebooting, changing some other system variables, booting back into a Controlled Start, etc. I unfortunately have never used the process (and willingly admit I'm not 100% sure it even exists), but I would suggest reaching out to CRC to see if they can walk you through the process.
On an aside; will changing a payload's values programmattically on-the-fly via the above quoted $PLST_GRP1.$PAYLOAD=(n) system variable set mess with the motion planning algorithm that FANUC has running in the background to calculate motor torque, current draw, encoder counts/speed rates/whatever type of PID algorithm they have going on? I always assumed that changing the variable as it's being used could cause corruption of the motion planner.