If you’re comfortable with a bigger investment, a duplex is good for the benefit of additional cash flow and you could house-hack.

Meaning, TIME, your gaining TIME.

So there might not be enough gain to need a 1031 exchange.If there is enough gain to justify the 1031 exchange then simply treat your replacement property as you would any other investment like @Daniel Osman said. 

Additionally, any existing restrictions at the town level (there are MANY) will be abolished, unless deemed "reasonable" by the state.

The biggest gains come from going all-in on one market and really getting to know it inside and out.

Additionally, an LLC can make it easier to separate personal and business finances, simplifying tax filings.Quick Tip: Work with a tax advisor to determine whether an LLC is the right structure for your investments.4.

Considering that, you are likely going to see appreciation year over year, which essentially will be additional equity you'd capture just by simply living in the home. 

Additionally, do you have any other ideas or strategies that might help achieve his goals without incurring a tax liability?

I know in residential lending you can get a HELOC to borrow a down payment to buy another property. Does this exist in the commercial realm? Current value of paid off property is roughly 350k , looking to borrow 75k-1...

This is only a guess, take it with a gain of salt.