Hi Steve,
Nice work on the cage, btw. What materials did you use, what is it sealed with, etc.?
It makes sense for you to try the 1/8" acrylic since you already have it. Not that big of a deal to switch over to glass if it does not work out.
I am using regular glass for my 1/4" double sliding doors and am happy with it. I did build a large cage for a friend and those have not worked as well. Part of that problem is because the stand he set the cage on is smaller than the base and has caused the cage to bow slightly.
I have heard of others having good success with 1/8" sliding doors that were "double strength". I'm not sure what double strength means, though.
Regarding the use of tempered glass, I understand there are some potential problems. All involve how the tempering process causes the glass to expand in an unpredictable manner. This can cause size variation which is a problem for double sliders. This is further confounded by the fact that the edges need to be bugged prior to tempering which makes the process all the more inaccurate.
To be fair, I have little first hand experince with this. I have asked for tempered glass doors with edges properly buffed for use in plastic door tracks. I was told it was possible but not easy and not guaranteed.