Does anyone have suggested property management companies they've used in Florida that they can recommend I reach out to, to see if we're a good fit for each other?

It sounds like the Title Co. was not aware that the tenant prepaid rent and just prorated the current rent for the month of closing, so agree if they had no knowledge of it, would not have ever gone on the settlement statement as a credit to the buyer and they likely will not do anything post closing to help obtain those funds. 

So, let's hope I get a recommendation.

. - We always recommend buying your first rental locally if possible and DIY managing to learn as much as possible before investing OOS.2) Lots of crooks and incompetents in the PMC world:( They both cost you money.- As already stated, you'll have a small portfolio.

If you are new and don't have a clue, then I would certainly recommend them or some company that can guide you through things until you have an understanding. 

I would recommend you begin researching Chicago based meetups as there are a bunch of really good ones.

BiggerPockets also has a calculator to analyze deals, and I highly recommend you start this as soon as possible, even if you are not ready to buy.

Does anyone have recommendations for a contractor for an almost full gut property in Rochester NY?

I recommend attending different Real Estate Investors Association meetings to network and get a feel for the landscape.

Based on the info in your post, my recommendation would be to turn these assets into well oiled machines and max out their NOI.