There is no particular reason to do your Roth conversion in two steps, unless you have two custodians. Yhen you will have to communicate your wishes to both custodians.
I hope the plan is to send all the funds into one Roth account so you will get rid of two IRA accounts and have one Roth account.
The best place for Roth money is a well-known self-directed Roth brokerage account (i.e. Schwab or Fidelity, not Robinhood).
There is no need to delay. If you have any earnings, that is taxable but that will be a small amount of money.
