but she doesn't want to have anything to do with it until I have everything up and running. Once it is, my contract is finished, and she needs full access but I no longer need to be able to access the solution.
It appears you answered your question already. You should provide her a copy of the file with the full access user account name and password when you are done. On your last visit to the file, set the password for the full access account to expire, which will force her to choose a new password the first time she logs in.
She will need filemaker pro to access the file. Filemaker pro advanced is recommended for developers, but you can do the basics without advanced. So you both will need a license.
The only point in hosting it is so you could both access it at the same time. It sounds like that's not what you want.
I suspected that's what we would need to do, but I couldn't figure it out for certain.