Depending on the size, I'd be happy to refer you to a good broker.

Are you comfortable with us obtaining references from your past landlords? 

No one has more "skin in the game" than a PMC as they have to deal with the property every day until an owner sells or fires them.Also recommend finding your own Inspector and not one referred by an agent.

For future reference I would work with lenders that specialize in mortgages for LLCs with short-term rentals. 2 that come to mind are Conventus and Visio.

What unfavorable odds are you referring to?

Reference HUD SFH 4000.1Lender needs to have experience with the 203k.

We specifically need someone who can do most the following repairsReplace Windows, Replace Doors, Bathroom Renovation, Minor Roof Work, Landscaping, 2nd Floor Deck Repair & Electrical Work.Would love a reference of someone who has done good work for you!

Any books you can refer me too that you read that is very helpful to you this day ?

The often quoted cyclical nature refers to MF properties, as developers respond to demand, build inventory until there is too much etc..The residential market does no go through cycles, just google homes values over the last 60 years.

Will they do all of the following:Ask for YTD paystub & W-2Verify employmentObtain bank statement to cross-reference payroll depositsVerify rent payments & lease violations with last two landlords and verify they are the property ownersMost won't.So, either learn to screen applicants yourself (plenty of source material here on BP including our blogs https://www.biggerpockets.com/member-blogs/3094/93296-how-to-screen-applicants-like-a-pro-part-1-verifying-credit-reportsOr screen & hire a PMC to do it for you.