Thanks for clarifying the question! If you wanted to keep it simple, the eastist and cleanest answer is to wait until 2024 to move the 401k to the Roth account.
However, with that being said, I don't see anything in IRS Publication 590-A that would indicated you have to use the pro-rata rules on moving non-deductible IRA funds to the Roth IRA in the same year you move your 401k funds to the Roth. The pro-rata rules only seem to apply when there are deductible and non-deductible contributions in any and all Traditional IRA accounts. In fact, the form used to calculate the pro-rata amount taxable in the transaction is Form 8606 - Nondeductible IRA's. In that form's instructions for part 2, it covers conversions from Traditional, SEP or SIMPLE IRA's to Roth IRA's, and rolling amounts from a 401k to a Roth IRA is not reported on this form.
So, if you rolled your 401k into your Traditional IRA which also has non-deductible contributions in it, then you would have apply the pro-rata rules. But if you rollover from an employer's plan to a Roth IRA, that is treated as a totally separate rollover from the IRA to Roth IRA converstions.
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