Swap which characters share palette

No, just giving Umaro commands will not be enough, he will continue to be perma-berserk. You need to apply a patch like Gi Nattak's Functional Umaro to allow you to issue commands to that slot.
https://www.ff6hacking.com/forums/thread-877.html

Note that that character slot will still attempt to use Storm, Tackle, and Throw unless you write some assembly to remove Umaro's special case with the Fight command.

As for your other question about palettes, it sounds like you're editing the palettes instead of changing the palette pointer assignment. I'm not seeing any way to change it in FF6Tools... that doesn't mean it doesn't exist, it just means I can't figure out how to do it.
What you can do instead is edit the values directly with a hex editor, or open a copy of your ROM in an incompatible editor like FF3USME and make the changes you need, and then make a difference patch. You'll need to figure out which values need to stay put and which ones need to be transferred, because both FF3USME and FF6LE will place data in other spots of the ROM for their workspace, data in places FF6Tools will try to use for something else. When you use LunarIPS to make the difference patch, make sure to set it to create a log and then immediately apply that difference patch to the copy you modified with FF3USME/FF6LE. That will tell you which ROM addresses were altered, which you can compare against the ROM map to see what needs to be copied over to your master ROM and what can be ignored.
https://www.ff6hacking.com/wiki/doku.php...sm:rom_map