" They seem to support it better than TurboTax. "
TaxACT is essentially the same as TurboTax.
It won't support two "Taxpayer" IRAs with a basis.
The only useful advantage it has is that it lets you edit the Form 8606 Name line when you try to generate a paper copy of your second Form 8606.
That can be printed and attached to Form 1040-X, as described in the above solution.
