Great post! I use screen a lot, and always miss having the other terminal histories readily available.
However, reversing PROMPT_COMMAND so that "history -a" comes first makes more sense: this way the last command executed on the current terminal has a better chance of being on top of the list for the next up-arrow (which more closely resembles usual behavior).
Also, as noted above, it's better to append to PROMPT_COMMAND rather than just overwriting it. Thus, my .bashrc now reads:
export PROMPT_COMMAND="history -a; history -n;${PROMPT_COMMAND}"
However, reversing PROMPT_COMMAND so that "history -a" comes first makes more sense: this way the last command executed on the current terminal has a better chance of being on top of the list for the next up-arrow (which more closely resembles usual behavior).
Also, as noted above, it's better to append to PROMPT_COMMAND rather than just overwriting it. Thus, my .bashrc now reads: