I'm thinking of scaling the numbers for the first nine seasons with the permanent numbers staying for the 10th season and beyond to allow for older players who retire sooner to have a chance to get in, Is this possible?

When does the game actually check the stats to see if the player qualifies for the HOF?

At the end of each season or at the end of the player's career?

It checks upon retirement.

I think you can change the HOF criteria in settings if you want to scale them.