[Cool Papa Bell]

Not sure if this works consistently or if it was dumb luck , but it worked for me in early season sims starting in 1901 or even 1871. I changed the minimum service years at start up to the max of 10 years I think it was in the league rules. I then erased the service time of all players in the other functions dropdown and assigned fictional financials to teams and fictional contracts to players in the financial dropdown. This kept players on their historical teams a little longer which was what I was after. Not going free agent too soon or being traded because a team was clearing cap space with an older player.

I was using a modified financial coefficient, but the result was that everyone was in their first year with a team and had the same contract values until they hit their free agency season. In case you try it, make sure you back up your league so you can restore it if you don't like the results. Have fun!