These are major red flags.

Here's my strategy - find a fully occupied triplex because for the reasons above, no-one wants them which means less competition in a red hot market. 

But being slow to evict and the whole deposit issue are big red flags.

After closing my insurance company flagged it and said I needed to take care of it now.

I wouldn't say it red hot but its pretty close. 

Too much red tape and administration to make it worthwhile.

From what I understand, there is a lot of red tape with 203ks, so I think you may be looking for a very specific contractor.

The big question is how do we not throw a red flag when all the sudden this LLC gets 30k of cash (dollars bills) into the account to purchase the property

In the areas we lived, single family had better margins and were in the area this caucasian red head who only speak english and german feels comfortable late at night ;) Since I self manage that was key.

Normally appraisers keep it in line with the purchase price to keep the underwriter happy by not sending up to many red flags with a higher than necessary purchase value.