Does the program provide any guidance about the amount of Roth rollover possible with minimal impact on my return?

A rollover has no tax implications ... money is simply being moved from one ROTH to another ROTH. 

Or are you asking about a ROTH conversion ? 

If so when using the online program all you can do is keep changing the amount you enter on the 1099-R screen using a code 7 in box 7.