Results from my Dolphin testing:
In order to find which Dolphin version introduced the real-Wii crash, I the typical range-halving method, and found that the first version to do so was 6568, whose changelog was simply "Set bMMU to true by default on x64". I then manually disabled MMU in that same version (right click the ReDux file and select Properties; I haven't found this setting on the global options menues), and sure enough, it didn't crash. Then I tried it with the latest release, 8783, and the same happened: the crash occurs if and only if MMU is enabled, which since 6568 is done by default (Dolphin's per-game settings have three values: checked/enabled, empty/disabled, square/default. The value of default for MMU is enabled, so emptying the square solves it and remembers it even after updating the game).
Not sure if this setting can be changed through backup loaders in a real Wii.