…I’d extend it thusly:

Set the tyre allocation for a weekend to exclude quali entirely, and for qualy give each driver two sets of tyres per qualy session like this based on championship standings:

1st - 3rd = C1 (Hardest)

4th - 7th = C2

8th - 11th = C3

12th - 14th = C4

15th - 17th = C5

18th - 20th = C6 (Softest)

This will give the resultant shakeup of qualy that people seem to like without feeling forced like a reverse grid.