Columns in the INCLUDE list are not part of the key. Crudely speaking and with the small amount of detail provided, your suggestion of an index with patientnumber as key sounds more likely to be useful for a query which filters rows based on this column, than the "covering index" described (why do you call it a covering index since it doesn't support the WHERE clause of your query?)
If you can post up the Actual execution plan for your query, folks will be able to provide you with a more specific answer.
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden