if im not mistaken all convertables or any other cars that dont have window frame attached to the door have different window regulator (with much stronger window support)
if you cut the frame the window will be supported by 2 bolts on the regulator and it is going to swing when you open the door , im not even talking about how easy its going to be for thieves to get into your car even with the spoon.

buy a door from scrap yard and try, actually you are the first person i know trying to achieve this, good luck.