Obviously if I was in minor and this was a cadence then a dominant chord would be used for ^2 and a i chord or i6 chord for ^1 but I cant use this because then the progression is going to make i sound like the tonic and I want to tonicize III. My thoughts are that ^2 would have to be harmonized by VII which has natural ^7 and implies the major mode but then what chord gets ^1? My harmony book shows that VII usually progresses to III and this chord cannot harmonize ^1. The only other chord from my notes that I can see that follows VII that has ^1 is iv6 but I am not convinced that this is the only option. Thinking outside the box, what about VI? Well I am not sure that can work because there would certainly be parallels in a progression like VII VI with ^2 ^1 in the melody. How can I harmonize this melody without sounding like I am going back to the minor mode?
FYI: I do not have access to the minor v chord yet which I believe would be helpful in harmonizing the ^2 but I wonder if I could label this chord as iii in the major mode which would justify its use? Then I could use I iii IV to harmonize the progression albeit in the major mode instead of calling the chords III v VI which is not a progression I have learned yet.