Roth to Tranditional to ??

I contributed $6,000.00 on January 1, 2022. I had an one-time unplanned for spike in MAGI(300k) from my business.

February 1, 2023  I finally figured out I was over the income limit for Roth IRA out when I went to file my taxes, as it gave me a warning and penalty warning. So re-characterized to Traditional for value of $3,541.78...which I have now figured out I am over the MAGI limit for traditional as well, so it won't be a reduction of MAGI and tax benefit.

 

Can I re-characterize back to roth as a backdoor, since I am not getting the benefit of traditional? Or did I mess that up?