There is nothing I know of in law that creates a cure for this situation. It might be possible, if the employer is willing, to re-issue your prior paychecks (you pay them back your salary and then they re-issue the paycheck with the different contributions)--but I don't even know for sure if this is possible and the employer would have to be willing. I don't know of any way to force them to comply. There is also no way to contribute directly to the 403b, it has to come from the employer. And (unlike an IRA) you can't direct contributions from January-April 2024 to be considered as retroactive to 2023.
I am also slightly concerned about the overall picture here. You can only contribute to an IRA up to your compensation from working. Are these grants considered compensation? If only your $600 per check is considered compensation, and you put that all into a 403b, do you have any compensation left over to validate your IRA contributions? I'd like another expert to comment on that.
@dmertz
