I am a CDI distributor, and I've sold hundreds, if not a thousand, of them. I have installed many of them. I've had a CDI or Schaefer Snapfurl for decades on my trailerable sailboats, too. And in those 20+ years, I have broken one extrusion (a dumb mistake) and permanently bent another (too lazy to take proper care to store it properly).
I have tested a bunch of leftover sections of extrusion for both the CDI and the Schaefer Snapfurl, and I can state definitively that you cannot straighten out a a kink in the extrusion by placing it flat leaving it in the sun, or by putting it in a black PVC pipe and leaving it in the hot sun. I define a kink as a bend in one direction followed by a bend in the opposite direction, or a sharp bend. with a radius of less than about 5 feet. Nor can you strighten a sharp bend out by bending the extrusion in the opposite direction.
Seriously folks, I have tested sections of plastic extrusion to the point of destruction! And I have never heard of a customer who successfully straightened out a kinked extrusion. I do however, sell a few replacement CDI and Snapfurl extrusions every year.
The most important thing to remember is that plastic furler extrusions MUST be stored straight, without any short droops in or revere bends in a row. What you need to avoid is a curve in one direction followed by a curve in the other direction. If you leaveit like that for a few days, it will be permanently noticable.
You can store it a) hanging by the ends from a rafter in a gentle, large diameter curve, or b) for a couple of days in the cabin bent into a very gentle u-shape, or c) lashed straight to the mast (or a pipe or on the ground) with padding near the drum, and with a support where the furler drum hangs past the foot of the mast.
If you last it to a mast or pipe, take care to use bungies or ties about every 12-18" apart so it doesn't droop inbetween the bungies. Also, if you have spreaders, lash the furler underneath the spreaders. Don't drape it on top of the mast and over the spreaders. If you leave the furler bent over the spreaders, the extrusion will develop a permanent deflection that you'll see when you're sailing.
It's a personal choice whether to remove the jib during trailering. I always left the sail on the furler and strapped the furler to the mast. Where it extended past the mast, I bungied a boathook pole to the mast. Leaving the sail on the furler saved me 15 minutes or more during setup and take down. The sail had a UV cover. Some times it got a few bugs on it when I drove past rice fields, but nothing that didn't wash off. Take care to avoid chafing a hole in the sail.
There were a couple of times that I put the furler inside the cabin for a long road trip cross country, with the middle of sail and extrusion sitting in the vberth and with the ends of the furler going aft on both sides of the a settee. It is not an "offically" approved way to store it, but the 7 or 8' wide curve in the middle never seemed to hurt it.
Leaving a gently curved extrusion straight in the sun is effective when you've have left the extrusion coiled tightly in the box for a week or two or more after it was delivered. That will relax the coil enough for you to install the furler, and the luff will be straight enough to use.
You can cover the drum with a towel (or an old crew sock for the smaller models) to keep it from banging on the deck gelcoat during mast raising and lowering.Or make a cover for it.
Or set up your mast raising system so it can't hit the deck, but that's a whole separate topic.