Ahh, the old convertible question.
Here's a little info about the great Mr2 mk2 design specs.
I'm glad you posted the convertible picture as this will help with the reason Extreme are able to chop up the Mr2 so much.
When the original mk2 concept was designed, it had to fill many criteria's one being the various roof options, so we have standard coupe, targa and convertible. The chassis is strengthened around the a pilla and rails to enable minimal alterations along the factory production line for all models, the original extreme murci designer went into great detail regarding the structural integrity of the car many years ago on this website.
If you have a DVD of the Murci build you will see that the roof is chopped completely off, there's a bit of either 20x20 or 25x25mm box section (can't remember) used from the top of each side of the window frame to the rear of the car just to hold the fibreglassed roof section.
D