In January 2020 I contributed $6000 from my checking account to my traditional IRA, then I converted this $6000 to my Roth IRA (i.e. backdoor Roth contribution).

In July 2020, my employment will terminate and the corresponding employer retirement plan includes a 403b (composed of both pre-tax and post-tax contributions) as well as a 401a (composed entirely of pre-tax contributions).

I would like to rollover all of my 403b and 401a funds directly to my Roth IRA (the taxes for the pre-tax to post-tax conversion would not be significant), but I am unsure if I can do this without penalty (March 2020 backdoor Roth conversion) due to the pro-rata rules.

If I’m unable to perform the above (convert all of the employer retirement funds into my Roth IRA), then the plausible alternative would be to rollover only the 403b post-tax funds into my Roth IRA, and rollover the pre-tax 403b and 401a funds into the 401k of the new job I begin shortly thereafter (rather than place these pre-tax funds into a traditional IRA, which would violate the backdoor Roth IRA pro-rata rules).

Any help would be greatly appreciated.