I've taken a preliminary look.  Impressive table size, 3+TB!  I'll definitely have some suggestions for possible mods to indexes.  I don't know if you be able to / want to...

1) Get a good book on SQL Server Administration.  I've found that those including Brian Knight or Kalen Delaney are reliable.  If you read it and study it, the book...

A few critical tables would be a good start, particularly large child tables that are currently clustered on an identity column.

Edit: Be sure to include any "missing index"...

DECLARE @Begin_Period int;
DECLARE @Last_Period int;

SET @Begin_Period = 201712;
SET @Last_Period = CASE WHEN @Begin_Period % 100 < 12 THEN @Begin_Period + 1 ELSE @Begin_Period...

The code below will produce two result sets.  The first is missing index stats/info.  The second is existing index stats/info.  We combine the two -- and often other needed...

Another option could be to use a static view that is dynamically generated for the formulas.  When a formula(s) change, the view is regenerated.  Just an idea.

The first focus should be on getting the best clustered index on all (significant) tables.  That is the single most critical performance factor for most tables.  Hint: This is most...

Looks rather straightforward, since the detail table already contains the Position the person was in on that given day.

If  you could post useable sample data -- CREATE TABLE...