Yup easier to get on with a regional and log part 121 time than try to impress the majors with right seat Cirrus time..... The learning curve for the MIL guys can be huge at the majors and the regionals is a good baby step.....
With the MIL back ground, upgrade at the regionals can be real quick... suggest some of the 'bottom of the barrel' outfits like Great Lakes, Mesa and Gojets....