There should be a train of gears between the the advance mechanism and the take-up spool, designed to make the take-up spool twist as much as needed to take up advanced film when yet empty.
To enable the take-up spool to turn less when it is getting filled, and thicker in diameter, a friction mechanism is located somewhere between advance mechanism and the spool, likely near the latter. Getting that friction reestablished should be the solution.

But as the original friction device failed anyway, why not trying an alternative method?