You don't "need" to shut down for the Inverter's sake. However, you might want to shut down for your sake. A lot of amps are at the bus bar if you haven't turned everything off.
My inverter can pass through PV and Grid, and leave the battery alone. So, I can turn off the Battery Breaker and keep power flowing to the house. Don't know if that is possible with the 6000xp.
My process is:
1) Charge up current (old) battery to full.
2) Turn off battery breaker of the Inverter
3) Turn off battery.
4) Attach new battery to busbar
5) Turn on battery breaker
6) Turn on new battery (it has a pre-charge circuit, but usually doesn't need it).
7) Charge new battery to full (added benefit that if you have done anything wrong, it won't charge, and you haven't turned on the old battery yet).
8) Turn on old battery
9) draw down on battery a little
10) charge both batteries to full