When a good buying opportunity arises, we'll simply write a check out of our line and purchase in cash.

To put it simply, you may be over complicating things.

The first deed is unrecorded.Also, if you can prove (recording checks, intake sheet, copy of all submitted docs/instruments) that the deed is in queue with the recorder and you are simply waiting for it to be indexed and returned, and you have a title commitment in hand, this should be a non-issue. 

Is there a strong chance they'll simply reject my claim?

this is all great advice you have here...I would simply add, spend a bunch of time..a bunch, on your tenant screening.

I get that certain areas just aren't good for my particular business plan, but I got a flat "I don't go there", "It is too competitive" or simply not addressing the questions I asked.

If you can not convince yourself why "this" method is better for you to do than "that" method you are simply winging it.So answer that question if you would, and lets see if your choices are sound ones!

Many folks stay right with their sweet spot and simply sell one and buy multiple replacements. 

@Lavon Newborn,You can setup an LLC yourself simply by going to your State Corporation Commission (at least that's what it's called in Virginia) and filing all of the required forms. 

Otherwise, it may look like you simply opened an LLC to skirt liability, which has a high potential of being pierced by a decent lawyer.