All your problems stem from using the wrong unit of measure (day).  Radically simplify the solution by defining a "relative" work week for each shift.  Create a table with the following...

The best programmers use almost no variables.  I think it can be simplified down to something like this:

declare

 @minutes int,

 @incr int

set @minutes = 29

set @incr = 10 --1,3,10

select round(((@minutes / @incr)...

After decades of maintaining stored procedures, I have evolved into always using aliases for less typing and higher maintainability and readability and faster, easier editing.  Since foreign key columns virtually always match the primary...