Here is an issue I've thought of with using tape or anything like Eternabond. Whatever you put on as a layer on top of the awning fabric ends up being a slightly different "size" when the awning is rolled up compared to when it is extended. That's because it is on the outside of the curved surface when it is rolled up and on the outside of a flat surface when it is extended. You wouldn't think this difference in size would be significant, and it wouldn't be - except if the material is completely glued to the underlying awning fabric. In this situation the weaker material - either the awning fabric or the tape - has to bunch up or stretch out as the awning is extended and retracted.
I installed my sunbrella while the awning was in a stored position. I used tape around the perimeter. All the sunbrella that is not taped is free to move. As I extend the awning I can see that the sunbrella pushes upward, away from the awning fabric, in the center area where the tape doesn't hold it down. The looseness of the middle portion gives it the flex that it needs in order to change size.
Does this make sense?
It isn't something I thought of while I was designing it. (I'm not that smart.) But it is something I have observed, and what I've written here is my explanation of what I've observed.
If the protective material were totally glued down, you wouldn't have the built-in flex that I have. I think that the stress this would put on the awning fabric, over time, might wipe out any benefit you'd be getting from sun protection. Maybe.
Bottom line - to address your question about which Eternabond to buy: in light of the above, I'd get the thinnest material you can get, in order to ensure that it is the most flexible.
-Speak