Best Time for Back Door Roth IRA Contributions

The answer may well be "never". You are likely in a relatively high tax bracket right now, judging from the fact that your income is high enough that you can't make direct Roth IRA contributions. In the past you probably picked a pre-tax instead of Roth 401(k) for this reason. By doing Roth conversions now, you're essentially reversing this decision. Generally this only makes sense if your tax bracket drops significantly, which it doesn't sound like is the case for you now. But if you're set on doing it, it's generally better to do it as soon as possible. Investments tend to go up in value, so the sooner you convert, pay the taxes, and get them into Roth the better.

You cannot process a tax-free "backdoor" Roth IRA contribution if you have existing pre-tax funds or earnings in any traditional IRA account.

If the amount of the pre-tax funds + earnings is low or you're in a low tax bracket, it may make sense to effectively convert the pre-tax funds to Roth at your marginal tax rate, but so long as untaxed earnings exist, you cannot perform a true backdoor Roth.

Note that some employer 401k plans may allow you to roll in pre-tax IRA funds. This is subject to plan rules and may provide a means for you to process tax-free backdoor Roth IRA contributions.

If you meet the requirements for a backdoor Roth contribution or are willing to pay tax on the existing funds + earnings, the timing generally does not matter, aside from any interactions with your other income in the same tax year.