Unless its absolutely necessary for you to put her in facing out, I'd just walk her in. It seems to me it would be safer having her butt on the butt chain and head toward the wall. If she kicked she wouldn't be going through Plexiglas or metal.
It just seems unsafe to have her facing out to me.
We have a wash rack that is similar and we walk them in and back out.
If you have to do this, try walking her in and backing out over and over, then turn her around and go the other way.