Thanks!
Actually I just figured out how to do it using the same method you were describing!

I was using the GUI version on Windows which allows the "XXX_down.bat" script to run, but it was locked to running before the tunnel went down (as it states in the OpenVPNGui documentation). However, when I placed the up/down scripts directly into the configuration file itself the problem went away.
e.g.,
script-security 2
up "run_me_after_I_am_up.bat"
down "run_me_AFTER_I_am_down.bat"
The man page also has an option "down-pre" which alters the behavior of the down configuration directive to call the script BEFORE the tunnel goes down.
Interestingly, it didn't matter whether or not I used "down-pre" in my configuration file, as the error message I was getting when using the GUI "XXX_down.bat" method no longer showed up (i.e., the ssh tunnel was brought down after the tunnel closed instead of just before).
I am not sure how these GUI scripts work, but it appears that they are NOT being added as command-line configuration options which get appended to your configuration file:
openvpn --config "my_config_that_openvpngui_called_on_my_behalf" --up "XXX_up.bat"
Rather I think they may actually call these scripts independently of openvpn. So, when I hit disconnect and try to close the tunnel it runs the "XXX_down.bat" script first then sends a terminate signal to the openvpn process. This would explain the behavior that I was getting - the script was being executed far in advance (in microseconds) than if the script was being called directly from openvpn.
What is funny is if openvpn can handle these directives in the configuration file, what is the purpose of adding this behavior to the GUI? The only GUI script that is relevant is "XXX_pre.bat" as that does not have a configuration counterpart (--up runs after). Using similar logic, it may be useful in some cases to have a "XXX_post.bat" which runs AFTER openvpn has completely exited (e.g., copy files, etc.). "XXX_down.bat" can be accomplished using the --down configuration directive (both before and after).
Well at least my minor annoyance is a thing of the past.
Thanks again for the help!