If I lump them into 1 LLC they would all be at risk in a lawsuit . 

It is my understanding that if you enter into the lease knowing of the foreclosure and placing a tenant anyway, then the lease is essentially deemed invalid as you and the tenant knew that it was a matter of time before they were evicted.Also there is an assignment of rents in residential mortgages as well, and doing this may open you up to a lawsuit by the mortgage holder since you essentially stole potential rent from them.And finally if the plan is actually to buy an HOA lien and wait until a foreclosure, I think that falls under unethical practices and would never do that, or encourage anyone else to either.

Would it all just be mostly the same: general background check (including prior evictions, lawsuits, etc), credit check, income verification, landlord references?

It is incredible that so far nobody has actually initiated a class action lawsuit on the Groves yet.

Well, not really.  But I have been before.  Now that I have your attention, I want to talk about your and my liability as property owners and what we can do to limit it.  
The first order of business when you acquire...

In addition, our new home will have an attached in law suite in which I intend to rent out as well.

A lawsuit was filed and an injunction was put in place.

So we look for sufficient capital reserves to be sure people stay out of lawsuits. 

-Should I put the property under an LLC (pay higher mortgage rate, but better protection against lawsuits) or keep under my name?

If the deal turns out to be a loser, you could have one co-bene refusing to sell, tying up the deal in a lawsuit to force a sale.