I'm a 4th year DO from NSU also going for allopathic surgery categorical residency (5 days to the match!). I also did my 3rd year surgery clerkship at Mt. Sinai.
I hate to be the bearer of bad news but I know for a fact that neither UM/Jackson nor Mt. Sinai will take a DO anytime soon.
At UM/Jackson I have a connection who is very good friends with the director of the program and she talked to him about getting me into the surgery residency. He said it would be no problem... so long as I transfered to an MD school. Plus, my school's director of the surgery department completed his residency at UM/Jackson and he will be the first to tell us that though he has tried hard to influence them over the years, they still won't budge yet on taking a D.O. for surgery.
As for Mt. Sinai, they've never taken a D.O. and likely won't for quite some time even though they take us for their clerkship (this is kind of like how they have a ton of IMG prelims but rarely take any for a categorical spot unless forced to like last year when they went unmatched). The current director and assistant director of the surgery program are really nice guys who are interested in teaching D.O.'s, and I believe if it were entirely up to them they probably would take a D.O. But the former Chair of the surgery dept, who is now the chair of vascular surgery is so strongly opposed to taking a D.O. that it won't happen so long as he is there. I'm sure there are also some other dissenters as well.
So nowhere in Miami is D.O. friendly for gen surg. The good news on this is that Mt. Sinai is not a quality program. As stated above, they are the only surgery program to go unmatched last year. The reason for that was likely because of their probationary status during the match, however their probation was NOT for work hour violations. It was because more than half of their chiefs in the past five years have failed their boards. And after doing my 3rd year clerkship there and then doing 4 sub-internships at other hospitals in the southeast U.S., I can honestly say that I am not the least bit surprised that chiefs aren't passing boards. Long story short, the residents are not getting the same quality training/education that residents elsewhere receive.
Your best bet for Florida gen surg would be UF Jacksonville (the only Florida gen surg residency that is D.O. friendly). However, they just got a new director/chair, Nussbaum who moved over from Cincinnati. I did a AI there and I worked with him and interviewed, but I honestly can't say I got a good feel as to whether or not he will continue their D.O. friendliness.