You are correct that the Traditional IRA balance will limit your back-door Roth contributions going forward. If you're amending your 2024 return, you could report this amount as a Traditional IRA contribution and include it in your back door Roth rollover (up to limit).
Say Yes to make/track non-deductible contributions, and make this amount a non-deductible contribution. Here's more info on IRA Conversions and Recharacterizations.
You're correct that your best path forward would be one of the two options you stated. The easiest and safest way to do this is to ask your trustee to move the funds internally.
Here's more on Back Door Roth Contributions.
@moses0020