The criminal history of the original petitioner doesn't matter for her. I missed the fact that she is also a visa overstay (didn't catch the 'over a year ago' in the original post). For that reason she would be best served NOT leaving the U.S. but applying for the adjustment of status with the I-130 per Fritz instructions. The bans on re-entry for a visa overstay only apply if she leaves the U.S. (the bans are on re-entry, not on adjustment of status).
A K1 entrant cannot have her K1 visa converted to Permanent Resident status (without leaving the U.S.) if marrying someone other than her original K1 petitioner. There are a few visas which were designed to thwart "conversions of convenience," and K1 is one of them. Other visa entrans who cannot convert status without leaving the U.S. are "C" visas, J1 visas (if with 2-year "outside U.S." requirement).
The irony here is that a B1 visitor visa allows conversion without leaving the U.S., even years after it has expired, as the result of marriage to a U.S. citizen.
But a K1 entrant is locked into marrying the petitioner or leaving the U.S.
I can't speak for Fritz' advice to use the I-601 process for waiver from "grounds of inadmissibility," but that might be the only option.
I used the I-601 procedure to obtain a visa for a Mexican national who had been in the U.S. without a visa, married a U.S. citizen and had children, but he had to return to Mexico for processing. Since then the I-601 processing has been enhanced and may be even easier to use (but there are fees).