Giving more details should help other members on BP give you a better recommendation. 

Hello fellow NY Landlords & Property Managers:We are seeking to potentially off-load up to three  of our 3-Family Buildings  in North/Central Brooklyn NY to a detail-oriented, will-stop-at-nothing-to-do-it-right Property-Manager (maybe one that specializes in 3-family townhomes & brownstones in Brooklyn). 

you gave 3 numbers and no other details (where, condition, comps, etc)I'll give you an equally simple answer.

The building has a HOA, but I don't have all the details.

just post the details of your deal here and you will get lots of responses. 

You need to look at it this way.Not all Bookkeepers are Accountants and not all Accountants are CPAs.Bookkeepers are typically just data entry with a little knowledge of accounting.Accountants typically have a degree in AccountingCPAs are licensed.Not all CPAs know real estate and that goes with Accountants too.A few times I had to teach a CPA to learn how to book certain items correctly.You want someone that show you the financials and break it down to you in details.

Below are the details of the loan request.

Talk to your lawyer about the details of how to properly transfer property into your LLC.

I realize that there could be a number of details absent from the listing that could tarnish this deal's luster.

I know that doesn't exactly address your question regarding the 3-plex being considered an investment property by FHA, have you talked with the loan officers about providing proof that your duplex is already fully rented out, to show your intentions of occupying the 3-plex?