Just some suggestions:
* You are only allowed to buy players with e.g. twice your TV income. Last season in division II I had 120k in TV money and more than a 240k guy would not make sense for me to have in the team. To base what you can on TV income would stop new teams from overspending on monsters. It would also stop them from renting a player to advance to a higher division where they again needs to do similar move due to their temporal strength.
* Only free agents on the market will be players with caps for their countries national or U21 team. I think that it would be better to raise the transfer price for players with a lower availability of high grade players. This approach probably would need to be done gradually as lowering the demand of players too much might cause economic imbalance.
* To stop the rent a guy phenomenon I would suggest both that you need to have money to cover salaries for three weeks and that you need to keep the player for at least 3 weeks. Renting a guy less than three weeks ahead of playoffs would basically mean that you must keep the player until you are out of it. Of course causes a problem. I don't really like the idea of forcing a player to stay in team for that long but it might be better than current system.
Just some thoughts.