Looking at your car with its design in mind, The A-pillars are the first line of defense and strength on a Hardtop aside from being the frame for the front windshield. The structural braces that run along the side and the cross dome light brace act as longitude support or spinal cord as they connect to your C-pillars where the roof line swoops down. All that area of the side windows (without a B-pillar)is just a big void where strength is non existent and could be at question when a car launches hard.

Contrary while looking at the quarter panel area on a Post Sedan, it pretty much is like a triangle of strength, with the Post door acting as a silent partner sought of speak.
But when a Hardtop comes into the discussion, it is an open horizontal V shape that is strengthen with the braces in the C-pillar and quarter window inner panels just behind the front of the quarters. The cross brace just behind the back seat gives the whole package some side load assist. The doors themselves are just a hanging panel that pretty much does nothing. The dome light cross brace is not too much of a concern but it helps the roof. If anything, I would go there with the Dremel tool.
Now if you cage the whole package, even with Chrome-moly, it pretty much puts back the same weight or more just to stiffen the car back to normal and make it safe. The cage in that case of course, stiffens the car, but then it is leaning towards becoming a chassis car.
I think that 30-40 pounds could be found on the front end still. You probably will not go with Carbon fenders or glass, but maybe some hard thinking will invent and desent the weight in another way.