Very late versions of v2.2 and v3.0 use a newly named location for the parent folder icon. The location was changed to prevent compatiblity problems when v2.1 is installed into another folder.
You should have no problem running v2.2 and v3.0 from different locations. Although v2.2 is a beta as well. Perhaps you mean v2.1? Although if you do mean v2.1 then it shouldn't matter because it uses an entirely different key.
I believe v2.1 uses
HKEY_CLASSES_ROOT\.FlashFXP_PI
HKEY_CLASSES_ROOT\FlashFXP_PI\DefaultIcon
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