My league just finished the super bowl. I have a few players that I would like to resign, and I have plenty of cap room for next season. However, I am unable to negotiate without changing the contract for the season that just finished, and I don't have cap room there. That makes absolutely no sense, contracts should not be able to change for the current season once the regular season starts. Is there a way to get around these players hitting free agency? This needs to be changed so that if you try to renegotiate with a player during a regular season, it affects only future seasons, and not the current one where contracts have already been agreed upon.

You can't sign a player to a contract without renegotiating their current contract. This is by design, players in the final year of their contract must be renegotiated in the current season or left to become a free agent to help guarantee they get market value.

You can try making some cuts to free up the cap room you'll need to extend your better players, the offers should be able to be submitted and the cuts will be processed before the free agent signings, you just don't have a guarantee that the offers will all go through.

Could he offer the current amount for the current season then increase the salary more than the given 5%. But then again the bonus would be more so his current contract would increase somewhat there

His base salary is prorated (at the end-of-season stage it's going to be zero but his current year will apply 100%) so his new bonus will be all that's going to hit your current cap.