OK, I looked at swapping the rec/reg today. Took a few pics that hopefully will help. No need to do anything with the battery or tray. Not sure what project I was remembering.
I think what I did was to remove the 2 bolts holding the rec/reg in place letting it hang free.

Unplug it from the wiring harness (my plug end is white so I had wrapped some black tape so it didn't stand out). It routes down past the battery tray.

Remove the bolt seen under the battery tray that is holding a wire keeper/support bracket.

That piece needs to be rotated and moved down the wire it is "keeping" and out of the way.
edit: OK, after looking this back over, I think I did take out the lower bolt for the battery bracket & rear brake line bits. The one needing a Allen bit seen in the pic. Making some wiggle room allowing me to have just a bit more slack on top disconnecting the rec/reg and routing the wiring.
Then pull the plug out & down from the motor and frame.Allowing the wire to slide down between the motor and frame with the plug outside.

Then pull it out the bottom though the area above the brake line parts seen in the first pick And the rec/reg will be loose, and likely on the floor. Reverse the process for installation.