I attempted to port my progress over by copying the entire contents of C:\Users\USER\Documents\Warcraft III\BattleNet over to C:\Users\USER\Documents\Warcraft III Public Test\BattleNet. The result was the game just shows a new campaign. I believe I left off in the middle of the TFT human campaign.
I believe the relevant file is Reforged.w3p. I decided to start the campaign on the public test server (just loading the tutorial mission and exiting) and I saw the file changed a bit. In particular I noticed HasProgress=1 changed to HasProgress=true. Makes me think it is not handling some legacy format but idk. If you would like the contents of my untouched Reforged.w3p file or anything else I can post that.