The last thing you want to do is have the courts decide who has to pay out who if you guys split.

If the owner sells it to you, they get to keep the proceeds after the loan is paid off at closing.

Hi,My goal is to get another rental property with the proceeds. 

If a seller wanted to take some cash (boot) out of a sale via buyer's passthrough, does this disqualify the seller's ability to 1031 exchange, or is that simply tapping into proceeds after downleg close that disqualifies an exchange?

I think that argument would carry in many court cases unless there is more to the story.I'd encourage you to have written requirements that you can make available to applicants. 

The more I have been reading, the more I am considering selling the 4plex and trying to do a 1031 into small apartment with the full proceeds because the biggest HELOCs on Investment Properties I have found after 26 calls is $250K.

Proceed with caution therefore.

He has other cash flowing properties and lives a frugal lifestyle so he does not seem too concerned about replacing the income from this property or have much plan for the proceeds of this sale.

You can't take an authorized occupant to small claims court or collections, but they are also easier to swap out. 

If you served them today to be out the end of November and then they didn't move and you are in court in December, they will ask for more time anyway (which the court would be inclined to give them some) and it will be January of February anyway.