I think these contacts that I just got will likely be helpful. I've only used them for a few days now. Now I think I have a good grasp on the technique for taking them in and out. There were a few things that made it difficult for me: I have small eyes, and I have strabismus, so that makes it difficult to get the lens and and judge the depth as I stick the lens on the eyeball.
It is my perception that I see more depth immediately after I put the contact lenses on. Last week when I had them on for a day, I seemed to have made good progress, but then it lazed down when I didn't put them back in. So I'm guessing and hoping that this is what needs doing.
Another thing I notice is that my esotropia does go down a little bit when I have the contacts in. I've always had that persistent esotropia. But I think this correction might help get rid of it once and for all.