For now, both are nicely cash flow positive and renters are literally clamoring/overlapping one another to get in them.

I am confident I can find regular tenants by renting to the interns my company employs for six months at a time (they over lap their internships so there's always an intern at the facility).

While there are a number of nuances to real estate, you don't need someone who does it only real estate in order to receive excellent service - there are massive areas of overlap between normal day to day operating businesses and real estate that a proficient business tax professional can navigate with ease.

There are others, and I don't believe they overlap.

Work overlaps the one on the 13th. 

Electric can likely be split easily if the apartments don't infringe on each others electric, you might need to look and see if there is any funky overlap.  

So pretty much I can just have seller credit me rent/prorated rent for overlapping, and notify Section 8 of the sale, and then follow up with section 8 to cover?

If you are sending out campains from different list providers, or even from the same provider but don't want an overlap of the same address, how do you scrub for duplicates?

You will be surprised at the amount of overlap.

I overlapped properties based on the years of accumulation and figured out how many mortgages I would have outstanding at any given time.