After implementing last meeting's tip that kept your history in sync between multiple terminals, Kris and I realized it didn't work as we had expected. We found more information on the history command that helped matters and we also realized that (as often is the case) it did work as we told it to, but not exactly how we expected it to.

So in the end we changed

PROMPT_COMMAND="history -a"
to the improved version
PROMPT_COMMAND="history -a; history -n"
Now bash writes and re-reads the history file every time it prints a new prompt for you.

Now we come to our misunderstanding of the way this works. Kris and I assumed you could type a command in one terminal and then switch to the other terminal and simply hit the UP arrow to see the command you just typed. It didn't work that way though. Well, the history is only written and updated when the prompt is printed. Swapping to the other terminal and simply pressing enter causes the prompt to be printed and the desired result of updating the history is achieved as well.