go to the: www.mcrgo.org
website and look at left menu for state reciprocity for MI CPL, and read what you might need to follow in the states you visit.
Some hotel safe are questionable, especially when I was in Hawaii for second honeymoon, the safe failed to open ten minutes after I was inside, due to dead battery. Of course, this was ten minute before the day tour was to start.
If the room safe is key lock then I might use it.
I'm hesitant about the portable lock box as you have, on the chance that your battery might be the power supply against the cable.
Maybe consider a installed safe??
Good luck and be safe!