A) Because the Roth IRA excess contributions are being corrected after the due dates of the respective tax returns, the correction of the excess must be accomplished with either absorption, a distribution of exactly the remaining excess amount, or a return or recharacterization of a portion of the $4,000 contribution you made for 2023. Absent getting your MAGI low enough to accommodate the entire existing excess as part of your 2023 contribution, simplest would be to just obtain a distribution of the remaining excess before the end of 2023, then in early 2024 contribute whatever you choose to contribute that still keeps you under the contribution limits. This is less prone to error than trying to do a return or recharacterization of some part of the $4,000 contribution.
B) Increasing retirement contributions to reduce your MAGI for the purpose of making a Roth IRA contribution is certainly an option. The amount that you are eligible to defer to the 457(b) for 2023 ($22,500 if under age 50) is unaffected by any other retirement contributions that you might make.
