Thank you very much! I am slightly non-trad. Graduated 2015, spent the past year as a research trainee/fellow in a translational lab (doing more basic science projects), am currently an Americorps VISTA in SC. I did not take the new MCAT because the 39 was my first attempt and I wanted to milk that as much as possible. Took it in August 2014 so I would be cutting it very close with the 3-year limitation from test date to matriculation, but luckily MUSC did not require me to take the new test.
And yes, I had my LORS in a few weeks before I'd finished my PS and activities...I'd thought about applying last year and had letters lined up so I just contacted those profs/bosses again and they were willing to help me out pretty early in the process. I procrastinated on the activities and PS so I submitted a little later than I wanted, but it looks like it's working out so far luckily!
*Edit: Also, secondary for MUSC for in-state residents is very short and includes a couple very short essay questions. I think for OOS applicants, there is more involved.