I think I finally got it in Device Manager. The trick seems to be to do it in stages with a restart in between. Move Com2 to a whole other address/IRQ, restart, move Com1 to Com2's old address and restart. After the restart Com2 can be moved to Com1's old address and then the swapped assignments will stick without conflict.
Thanks for your suggestions Tom, unfortunately you are a lot smarter than my BIOS which only does a global enable/disable for the ports.