Clustered Primary Key that is never used vs. Non-Clustered Primary Key on Multiple Columns
I'm working on a similar problem right now except more columns and millions of rows. We have a PK that isn't used in any queries. We ran a preliminary test where we changed it to a non-clustered PK and I found two columns that are used in where clauses and created a clustered index on those.

Many queries ran faster and out of more than two dozen indexes on the table we think we will be able to delete 25 of them.

In theory what were are looking to do is not best practices because the columns aren't unique that we're looking to use for the clustered index. But in practice it allows us to save a lot of space by making many non-clustered indexes unneeded and improve I/O by deleting these indexes.