I scheduled meetings with professors who wrote me letters last time, as well as new professors, to go over my application and pick their brains on what to do differently next time around, and I also asked them for new letters. Most of these professors sat on graduate admissions committees and were able to give me some insights into what they like to see from applicants. Their process is certainly different, but common themes are applicable across professional school admissions.
If anything, meeting with them again and detailing your reapplication experience is a "new development" in your relationship, and they can certainly speak to your tenacity, determination, perseverance, resilience, etc.