Benjamin,
I average 7K miles/year on my Speedster. I drive all year as long as long as it's above about 45 degrees. Never in the rain, if I can help it. I live in DC so our summers are hot too -- but nothing like what you'll face. I'm 6' and the car feels like a coffin when the top's up.
Changing lanes to the left is easy. Getting safely back to the right is problematic. Pulling out of a parking space to the right into traffic is a life and death decision.
Here are some ideas that probably won't help:
Buy a right rear view mirror with the wide-angle lens. It gives you a much wider field of view. Sorry but I can't remember the name.... oblique? I have the Aero style mirrors. There are some that are much larger and would improve visibility. But they will raise design questions regarding aesthetics and appropriateness.
You can get these attractive clip-on side vents that are attached to the windshield. I don't own a pair but I think you have to remove the door windows to use? Or does the Beck have roll-down windows. Regardless, they would bring in lots of air as long as you keep moving.
You mentioned quarter-panel windows in the top. That might work though I doubt it. Here's why. When you need to go right quickly you need to look to that quarter panel. But that panel is low and not wide. You'll have to crunch down and turn and look. Better than nothing possibly but I doubt you'll be satisfied.
I've seen tops that have rear windows that wrap all the way around practically to the doors. That might work.
Lastly, silly perhaps but routinely apply that solution to your windshield, mirrors, side panels and rear plastic panel that keeps raindrops from forming. Rainguard? It does help with visibility when it's raining. It's funny but I find that if there are drops on my mirrors, my eyes focus first on them before focusing on what's beyond them. That second or two to adjust will be important when a quick maneuver is required.
Hope this is helpful and enjoy you new car.
Marshall