Aha!

Found a solution, although it's kind of bizarre. I think something during the update corrupted Wineskin preferences, although I don't know how/why.

To fix it, I had to manually run Wineskin. So, from the terminal:

cd /Applications/MoI v3.app/Wineskin.app/Contents/MacOS
./Wineskin

From there, I clicked on the "Advanced" button, then clicked the "Test Run"

It's slow, and it spits a number of scary error messages:
2015-04-12 20:55:20.838 Wineskin[1938:63563] Debug Mode enabled
2015-04-12 20:55:20.853 Wineskin[1938:63563] Wineskin: Starting WineskinX11
2015-04-12 20:55:20.853 Wineskin[1938:63563] WARNING!!: You are running Wineskin on an unsupported OS and there may be major problems!
2015-04-12 20:55:21.691 Wineskin[1938:63563] Wineskin: WineskinX11 Started, PID = 1959
2015-04-12 20:55:21.989 Wineskin[1938:63563] Wineskin: Starting Wine
2015-04-12 20:55:22.745 Wineskin[1938:63563] Wineskin: Wine Started, PID = 2003
2015-04-12 20:55:28.351 Wineskin[1933:63561] NSAlert is being used from a background thread, which is not safe. This is probably going to crash sometimes. Break on void _NSAlertWarnUnsafeBackgroundThreadUsage() to debug. This will be logged only once. This may break in the future.

From there, MoI comes up cleanly. I don't know what Wineskin files get modified when doing this, but after doing this, I can run MoI directly again.

It did at least touch a binary Wineskin preference file in ~/Library/Preferences/[long number].wineskin.prefs.plist, and [long number] is different than the number that was reported in the error log posted above.

I hope this helps someone else.

___Samuel___