Hi @amensching, welcome to the 
community !!
Regarding your question. Have you already tried to give the users with limited viewership permissions ?
Also, found a somewhat similar post as might give you more info.
https://community.grafana.com/t/limit-users-to-access-variable-values/8513/2
Other than that, Although not possbile exactly when defining the variables as “custom” but when using the “query”, there is the option of Regex.
Maybe use the regex to filter out the list of result you want to show when they pull the drop down and the query gets executed in the backed ?
e.g.
