Buy current primary residence with 1031 - then refi?

[Gwen St. Pierre]

Hi there,

I am selling a rental property (H1) and would like to avoid paying capital gains. I would like to refinance my current primary residence (H2) using the profit and turn it into my next rental property. Then, I want to pull out equity from H2 to purchase my new home (H3.) 

Can I:

• Move income from sale of H1 to 1031
• Refi H2 using that money to pay down loan amount.
• Take equity out of H2
• Use that money as a downpayment for a new primary residence H3

Now that I type it out it seems like some hoopla the IRS would not allow - but my brain won't rest until I ask the question.