I'd rather get a HELOC and use it for the next 10 years when I need it rather than pulling the money out and not necessarily having anywhere to put it.

As easy as this sounds, it's not simple and usually like pulling teeth.

I just want to add that with delayed financing you have to use your own cash or HELOC ( I know you said cash, but making sure it wasn't hardmoney or any type of loan. ) Also the beautiful thing about delayed financing is they treat it like rate and term as you're not pulling more money out then you purchased it. 

Our only problem is pulling conventional loans via our business, as it doesn't provide income in an orderly fashion like banks and standard lenders prefer.

Then, I want to pull out equity from H2 to purchase my new home (H3.) 

lol Well, it's because those bozos pull crap like that the first chance they get.

When I pull into the parking lot or if he sees me coming out of my home, he runs into his house quickly.

Like @Rob Massopust said, pull your report and look for inconsistencies.

I have it in my mind that I would do "3 strikes" meaning that I'd put in an offer and at least 2 additional counter counters before pulling the plug. 

It's about you and your ability to pull off the BRRRR.