IMO you are not in the clear yet. The converter in a 2001 rig is likely one that should be doing 13.6 or so. Outside chance it is a 9100 and can do 13.2 but not until it has sat for a while at 13.6.
Find the battery lugs on the DC fuse panel inside the rig and take the converter voltage there. Should be 13.6. Then at the battery should be almost 13.6 with a full battery.
If still 13.1 suspect corrosion at connections--especially that battery neg ground wire at the frame.
You might want a better converter to look after your new battery, but IMO first get the wiring etc for this one cleaned up and working right. On that, be sure your new fuse/circuit breaker can handle say 60amps for any new converter you might get in future. That original corroded one may be too low in amps for that.
