I didn't look at every step in detail, but one step that looks a little sketchy to me is the replacement of the tertiary tosylate with cyanide. Certainly if it worked you could hydrolyze the cyano group to an acid, but the actual replacement might not give entirely Sn1 as you're hoping.
There are two issues: 1, that tertiary tosylate may undergo some E2 reaction, rather than ionize. Typically E2 reactions "require" a strong base, but this is an extreme case where you're using a somewhat weak base with a tertiary leaving group. 2, if it does ionize significantly to form a carbocation, then you will probably get a mixture of E1 and Sn1. Maybe it would work but it would probably be quite solvent dependant, and you'd want to use a very polar solvent to encourage carbocation formation, while still being careful to not use a solvent that would react with the carbocation in undesirable ways.