Tex68w makes a very good point. The good 270 awnings are both heavy and they do put a lot of strain on the mounting points. Fiberglass is probably not going to be happy.
I have been running an EZ-Awn Bat 270 on the fiberglass Snug Top shell of my Power Wagon for about four years with no problems. Until a few months ago it was mounted to standard Yakima towers and crossbars, three pair of towers in the Yakima 60" tracks. Those crossbars also carried an old school Con-Ferr steel basket with a 13 gallon water tank and four MaxTrax and sometimes decoy carts and bags of assorted crap strapped to the basket. The fiberglass is not only happy, it is ecstatic, because I just installed an even bigger rack system to carry all of the above and still have space for a 100W solar panel.
Re the question about awnings that don't have to be rolled up, the Bat 270 just swings out for use and swings back for storage, no rolling required. You don't even need to drop the legs if it's not windy. If the trailer is an issue, just swing the Bat 270 back against the side of the trailer and secure it with a bungee or a Quick Fist or even a strip of velcro on the side of the trailer. Then you can still use the full 270 coverage when you are not pulling the trailer.