I after even more study, Im trying some things. I'm going to leave this up so people can see what solutions I'm trying.
I have two things Im trying to do to fix my problem. First I got a string called 'LvLName' and had it update to whatever the TextInput had in it on 'SaveButton' pressed. Then I added a OnItem LvLName Set condition for Go To Layout LevelSelect.
I think the first problem was caused by the KEY slot being unnamed. It should make a new slot available if string from new, or it will just update the save of that name.
The second problem was likely that I was moving on before it was done.