Such is the problem with dealing with excess Roth IRA contributions when you are in the phase-out range of the contribution limit.
Your suggested approach is simplest and will work as long as you will be eligible to contribute at least $10 to your Roth IRA for 2024.
If you are unsure if you will be eligible to contribute $10 for 2024, pay the $1 penalty for 2023 and make a regular distribution (not a return of contribution) of exactly the $10 excess (with no adjustment for earnings) after October 15, 2024 but before the end of 2024 to resolve the excess for 2024 by being included on your 2024 Form 5329 line 20. This $10 regular distribution would be a tax-free distribution of contribution basis. Once you have prepared your 2024 tax return you'll be able to determine how much you can contribute to a Roth IRA for 2024.
