hmmm ok Scott not seen your experience on any of the remotes I manage.
In its defence I dont get the black screen problem with ALL headless.
Its just something I have come across. My experience doesnt just effect LogMeIn, it effects local Screen Sharing, GoToAssist....pretty much anything that has to redraw the screen remotley.
Having logged onto the effected black screen Mac via SSH and performed a
ps auxwww|grep loginwindow
and then
sudo kill -9 <root process>
the login window will then immediatley appear!
I briefly test drove GoToAssist with the intention of swapping my remote tool (for its ad hoc support distribution Vs. LMI) but it had more glitches than I could put up with and the headless thing could NOT be solved on ANY of the Mac Minis I was connecting to.
I'll keep a look out for your glitch and see if I can replicate it.