And the connector hooked to the servo must also fit with no slop. The entire exercise here actually is focused on first removing the slop, then giving the elevator horn enough lever arm that any slop at that connection is miniscule compared to that lever arm length, and then giving the servo some help by making the connection there slop free and close to the servo.

Good luck but.........
with all this advice, you ain't gonna need luck.
(and you've already shown IMMENSE patience to have read through all this....