Not the cheapest 25% or the most expensive 25% but I’m the middle, where people want to and can afford to live. 

Generally speaking it is somewhat true in the Bay Area (unfortunately).

There are options to work with the title company after purchase (60 days) to buy it with conventional financing and then shift the property into an LLC with a quitclaim deed to get the same effect as purchasing with your LLC but you get the advantage of better rates with the conventional loan.

Was going to say the same thing as @Jarret Jarvis for point #1.

While the interior is nice, the first-floor kitchen and bath are original from the 1940s.

Once the HELOC is in place, your father-in-law could loan you the funds to invest in real estate.

And if the latter... why?

You could put it on the market (and you'll know what that second assumption is), and at the same time do whatever you can to get the tenants out (and know what the first assumption is).

The seller had until yesterday to sign the document.

If so, maybe wait a year or two and save the money for the purchase.