Duplicate your Gamemode_Speedkart add-on to avoid the auto-updater. Rename it something like Gamemode_Speedkart2. Extract the gamemode.txt and description.txt. Edit the description to show a new name so you can identify it later. Edit the gamemode file. Under the line "ADDON GameMode_SpeedKart," add this:
ADDON Vehicle_SpeedKart
Put both files back in your archive.
The datablock and UI names of the new speedkarts seem to be the same as those of the original, so it should all work.