Good mornin,,,you can send a request to Alliance for diagrammatic elevations on the exterior walls of your trailer. Need to include your Vin#, year, make & model #. I have found them informative,,,once you have them you can call & discuss your questions w one of the responding techs. Response is usually pretty quick w/in a day or two I’m most instances in our experience! 👍😘🍀!
Can you get a small needle nose pliers on the screw body? Must be into some solid metal backing that was too thick for the small self taper screws if the screw heads broke off,,,if you can get the other non broke off screws out can you gently pull awning away from the body a bit to get the needle nose onto the damaged screw shanks?
I've had success with needle nose vice grips. Tightly lock them on the broken screw. Then hopefully you can just unscrew the screw with the vice grips.
Imho feel your caution the Azdel risk is very good advice given the size of the broken screw shank & the fact the screw head sheared,,,believe original installers use screw guns on these instalations whereas if they were hand tightened they would not strip or shear as readily,,,,have used your chuck solution several times on other situations successfully but agree that may not work w the rail still attached.
I have used it on wood, metal, and Tapcons in masonry. It has failed when there is not enough shank to grab on to...the amount of shank you need varies. Pine, not a lot. Masonry, in my experience, about 1/4" minimum. One of my buddies owns a carpentry company and shared that trick years ago.