I went through my configuration thoroughly and simplified things.
No more Song Menu.
No more System/Preset and System/Song entries.
Disabled Start Up on Last Preset (didn't work reliably).
Removed some weird data from the Exp.Pedals configuration.
Disabled Direct Send.
Removed IA Links.
And the issue hasn't occurred since. Sadly, I'm not sure what did the trick.
No more Song Menu.
No more System/Preset and System/Song entries.
Disabled Start Up on Last Preset (didn't work reliably).
Removed some weird data from the Exp.Pedals configuration.
Disabled Direct Send.
Removed IA Links.
And the issue hasn't occurred since. Sadly, I'm not sure what did the trick.