It seems you do indeed have the proper clustering key.

Next I'd look at the missing index stats from SQL. You may be able to cover a large % of queries with relatively few INCLUDEd columns; if so, great, do that. In general, consolidate covering indexes when you can. Yes, the rows are wider, but the data is shared between queries too.

Even then, you'll of course still have the issue of queries that use a non-clus key but aren't covered by the non-clus index. Those will take further review.

Btw, if you INCLUDE enough columns in a non-clustered index, you have effectively created a second clustered index, but, as you noted, with the increased disk space usage that requires.