I should probably read over the whole topic, but its not been edited into the main post yet so it may be new.
Just on a whim I tried the Classic mode, and as stated crashed after talling up the coins after the credits. But I tried a second time, this time during the tallying at the end of the credits I hit the reset button on the wii (not the power) which knocked me back to the "dont whack people with the wiimote" screen, then it starts to load the opening movie, but before it does a message pops up saying something along the lines of "Congratulations on beating Classic mode for the first time!" and the items I picked up on my play were next to appear, including the trophy of the character I beat it with.
So the jist of that is simple, reset the wii during the credits and it will save your progress in Classic mode.
Now I don't know if unlocking characters will work this way, or if the battle will only appear after the credits, or if you can just get the needed completes and do a normal vs brawl to make the encounter happen...but I'll get there eventually and let you know.