I really like my + controller... it's bright, it's integrated, it's fast to setup.

But... there are times where an outboard computer (iPad) would be very helpful with the larger screen.

Is there any reason I can't run both a + and standard controller and just bind them back and forth depending on what I'm doing?  I assume the only main thing I'd need to be mindful of is firmware versions matching between everything?

What happens if a maximum altitude (or other setting) is set on controller A, then controller B is bound?  Do the settings on the iPad software upload into the drone?  Or does the software read the settings from the Drone that were set by Controller A?

No reason at all, plenty of others have done exactly that.
Settings like max altitude, RTH height etc are stored in the Phantom, not the controller so no problems there.

Do not worry, the P4P controller and P4P+ aircraft are compatible. Please make sure all the firmware have been updated to the latest version and link RC. Changing RC will not change the max altitude.