Ok, took a while, but here is the second part of the fix. So the metal plate reflects a lot of the light and will keep the plastic housing from melting. There is still a small chance of the paint melting or burning a bit on the steel plate however, which wouldn't look too good. In our quest to permanently remedy this issue, the other member working on this with me suggested that night shading the back of the turn signal lens would likely yield the result we were looking for, as well as add a cool look to it. Results:
That is two coats of nightshade on the back of the projector lens for the turn signal. You may be able to tell, the stock HID projector lens has a bit of a tinted/darkened look already so it fits in nicely. Any heat that will be transferred to that lens/through it won't affect the nightshade, it handled the baking in the oven no problem and the spot at the back of that lens doesn't get very hot anyways. Even less so with the nightshade on there.
Turned out great, the turn signal is still plenty bright and as you can see there is next to no reflected light onto the shroud even when the sun is shining right on it. It is even possible that nightshading the back of the turn signal lens alone would be enough to stop the issue from happening, but with this two pronged approach you are dead certain it is fixed. I hope some others find this useful as it will allow people to keep doing this awesome looking mod without any fear of issues down the road.