Don't tender arbitration unless the player is critical and worth it going forward. Try to sign the critical players at a number that anticipates the following years arbitration.
Don't offer marginal pending FA more money because you are afraid they will walk. Let them go to FA and sign them or other players to deals that make sense.
Waive trade or release any overpaid player that you can't guarantee will make a difference. This is not easy but worth trying.
Use the shop player function then the trade screen "make this work" button to find out if the player you want can be obtained for a different player. This could be a cheat if overdone but it simply replicates GM discussions where you offer player X reluctantly, the other GM has player Z but is willing to take player Y or A or B. Up to you to make it a defensible trade.
Look at your minor leagues to find possible position backups at league minimum vs having to sign marginal backups at an elevated dollar value.
Watch the FA list dwindle and look for a reasonable player who missed the market.