Well, first, congratulations on figuring out what was going on. 🙂 Really nice work!
As far as where to go from here, you have a couple of options. First, you could try another plugin that does something similar but is known to work well with our plugin. Members would be a good option: http://wordpress.org/plugins/members/.
Alternatively, you could try to act as the go between to try to figure out where things are breaking down. Since our plugin has about 10 times as many downloads as the one you’re reporting a conflict with, we’d appreciate it if you’d ask them to take a look at where their plugin may be gumming up the works on the admin side. They can download a copy of the free version of TEC here: http://wordpress.org/plugins/the-events-calendar/
I’m glad that we’re getting closer to a solution for you, runwildmissoula!