Re: 2-stroke electric starter??
Yes, I am not suggesting that the specific arbor shown in the link would work directly, but it gives an idea of what type of contrivance would be needed to extend the shaft.
Of course the scooter mechanics would suggest a new shaft or engine, or whatever, because they have $$$ in their eyes.
But, with a little bit of ingenuity, I am sure that a solution can be found.