Is it possible to "convert" my EdD into a PhD, now that the university I went to offers a PhD in education?
I would petition the school. The same happened to me when I went through the Ed.D. program, and then right after graduation, they became a Ph.D. program.  Because many of my credits were transferred and I did the dissertation through the new school, they originally issued me a Ed.D.; however, my credits and curriculum more closely matched their Ph.D. program. Once I petitioned, they as of this week, converted my Ed.D. to a Ph.D. and reissued me new transcripts and a diploma with the original date of my Ed.D. on it from 2016.  I think it's possible, it's just that many people would not go through the rigor to request it.  Good luck!