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Look at early RT-10 Vipers for some inspiration.
In their early days, everything was an option. All the normal stuff of course. But the hard top, windshield wipers, and even the steering wheel was an option in early Vipers. Some came with a removable cloth top w/ clear vinyl windows....like a Jeep Wrangler soft top.
(Only thing that dissuaded me from buying a Viper in my price range before I got the Vette. All the newer ones I could easily afford had that terrible cloth top, and I wasn't interested in an older one.)
In 1989 I had a Mustang convertible LX 5.0 5spd. The convertible top rear glass section would unzip and lay in the space below the roof and between the back seat. Giving you a convertible bimini. Find a top if available where the rear glass unzips. I believe AORoads posted the same idea but with a roll up design rear window, maybe plastic. I remember at first I didn't understand why I would want to unzip the window, but then I started to do it on hot days where direct sun was too much, and I wanted the open air. Actually a great option to have day or night. Good Luck.
In 1989 I had a Mustang convertible LX 5.0 5spd. The convertible top rear glass section would unzip and lay in the space below the roof and between the back seat. Giving you a convertible bimini. Find a top if available where the rear glass unzips. I believe AORoads posted the same idea but with a roll up design rear window, maybe plastic. I remember at first I didn't understand why I would want to unzip the window, but then I started to do it on hot days where direct sun was too much, and I wanted the open air. Actually a great option to have day or night. Good Luck.
That IS what I was thinking of, but I guess the OP doesn't want a convertible car with a feature like that.
So.....that leaves a targa with a removable top and a replacement top that is "canvas?????" I guess it would be stretched within a frame of some sort and locked in place.
To me, the way this would work best is if somehow the rear window could open, too. But that would be major-major since it's not a notchback like the Fixed Roof Coupe (FRC) of the C5 era.
The very early C3s had a removable rear window, but no "canvas" top.