Critter-3's reply is incorrect. The requirement that the funds rolled over to a 401(k) be from a so-called "conduit IRA" was eliminated more than 15 years ago.
@mw104 , what you propose is permitted and is the only way this can be accomplished. You'll need to determine the amount of pre-tax money to be rolled over by subtracting the amount of the basis in nondeductible traditional IRA contributions and request that that amount be rolled over to the 401(k); as you indicated, the IRA custodian has no way to do this calculation themselves. Although such a rollover is usually done as a direct rollover with the IRA custodian paying the funds directly to the 401(k) plan for your benefit, best done by specifically identifying the particular 401(k) account into which the funds are to be deposited, but the rollover can also be done indirectly. Be aware, though, the the 401(k) plan is not required to accept rollovers from IRAs, so be sure to check with the plan before attempting any such rollover.
If you do a direct rollover, for that you'll receive a code-G Form 1099-R wit the IRA/SEP/SIMPLE box marked separate from the Form 1099-R for the distribution that is converted to Roth. If done indirectly both distributions will be on the same Form 1099-R and you'll need to split the form into two for entry into TurboTax because TurboTax cannot handle entry of a single Form 1099-R that shows both of these transactions. TurboTax automatically excludes the rollover over from the amount reported on line 7 of Form 8606.
