Why don't make unavailable the money till the transfer is really concluded?
With this simply rule we can avoid early bid and unfair bid wars.
The ability to use money from a pending sale adds a great deal of liquidity to the market. If you had a player who might be worth $3 million, your market would be limited to teams with $3M in cash, and would cut out teams who have $1 million in cash and a player worth $2M.
It would be difficult to hold off completion of the first sale, until the 2nd sale is completed, and besides the 2nd sale might be contingent on a 3rd sale, etc.
You could let a buyer take a loan from the bank. But you would have to have some way to evaluate your ability to repay to loan, either through ordinary revenue, or a sale of a player. If you could figure out a way to do that, you wouldn't need to have early sales. You could go to the bank and borrow $3M to bid on the player you want to buy, with some repayment schedule, and some of your players as collateral.