Deuteroprotos is simply second mode modulating into first mode (think of the melodic line αναστάντα εκ νεκρών in the second eothinon doxastikon in the Anastasimatarion of Ioannes Protopsaltes). The soft chromatic scale with basis Δι (i.e., the argosyntomos sticheraric second mode) predominates, but with frequent modulation into the diatonic scale with basis Πα (i.e., first mode) indicated by a phthora. The Δι of the soft chromatic matches the Δι of the diatonic, so the modulation is fairly easy to accomplish correctly.
I hope someone more knowledgeable than myself will give you a better, clearer answer than I've given (and will correct any mistakes I've made), but I hope this at least points you in the right direction. May God bless your efforts!
