It works perfectly, at least on paper. Has anyone else ever used an approach like this? Or is there a better way to do it?

It's the correct way of doing it... You are essentially multiplying with (1-friction) every time step so over multiple time steps the "correction" is (1-friction)^n and not n*(1-friction) (1-n*friction) as you would get with the first version when increasing the timestep n times.

Edit: n*(1-friction) would be totally off

It works perfectly, at least on paper. Has anyone else ever used an approach like this? Or is there a better way to do it?

It's the correct way of doing it... You are essentially multiplying with (1-friction) every time step so over multiple time steps the "correction" is (1-friction)^n and not n*(1-friction) as you would get with the first version when increasing the timestep n times.