If the Relative Finder app is limited to 16 generations, it is likely to be a limitation in FamilySearch Family Tree's API. The obvious clumsy workaround is to go back as far as FamilySearch will let you go, find the person who is a descendant of your person of interest, and run the Relative Finder or calculate the relationship of those two people.
While the FamilySearch API is closed to the public (per App Approval Considerations), I suggest looking over the developer resources at FamilySearch (e.g. the API resources). I see there that My Relationships, the "Set of how the current user is related to the passed in person." is marked as Deprecated, and the Relationship Finder "Find the set of relationships that show how {pid} is related to {opid}." is marked as a Prototype. Perhaps reading the docs will give you some clues as to how to find a better workaround.
Another possibility might be to try a software program which interfaces with FamilySearch, such as the free RootsMagic Essentials, fetch the data from FamilySearch FamilyTree, and use the Relationship Calculator or other tools in that program, unless they too are limited to 16 generations.
If you are interested in discovering how many different ways you might be related to this distant relative, consider putting your data into a graph database and using the path tools to show the connections.
Whenever you find a person of interest on FamilySearch Family Tree, I think it's a good idea to bookmark that person (as I write this answer, it is called 'Following'). You can choose to have notifications about when other users make changes to the profile. Another option is to save the profile's ID to your genealogy software or in a research log. Profiles do get deleted, but if you put the deleted ID into the search, FamilySearch's Family Tree is supposed to redirect you to the new profile.
I also like to print out a Family Group Sheet with sources whenever I view a profile, so I have a record of what I saw on a particular date when I visited.
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