would it be possible to redesign the chassis to have a hardtop and proper doors. by removing the top chassis rail and adding a full roll cage.

would this weaken the car too much or would it add strength since your increasing the neutral axis only thing is you have no cross bracing were the door would be.

would it add too much weight or would the aerodynamic advantages be greater than the increased weight

Personally I think it could work, the extra weight is not worth bothering with, about 10lbs?

Might well work - particularly if you make a steel panelled transmission tunnel as well as the roll bars.

But I would definitely get a FE analyses done before doing it.

FE analysis??

is that some kinda software modeling?