Instead, I'd like to sell this property and take the proceeds and roll that into a rental that's closer to me and use whatever tax advantages I can to assist me.I'm confused with how the 1031 works and was hoping someone could explain to me how to "use" it.  

HELOCs are advantageous for this reason, because if you do a cash out refinance you're paying interest on that money all the time instead of on the occasion when you use it. 

So, no timing advantage.

I know some have training programs etc but is there a huge advantage working for CBRE or Marcus & Millichap vs a successful boutique focusing its effort on a specific prop type in only a few cities?

The advantage of not having her own the property is if down the road she needs care it is income to her and not a straight asset.

In reality there are no perfect rules and sure Peter Thiel use the system to his advantage [and arguable broke the law because there is already a rule that prohibits stuffing your IRA with grossly under valued securities and no one seems to ask why the IRS didn't go after him for that] but is the societal cost of this happening one or two time greater than the benefit of the thousands of others who use their IRAs to invest in non public securities?

Are there advantages to one over the other?

@Alecia LovelessSeems as if it would help..Chatting with the lender they should give an honest answer as to which would be most advantageous to you.

We are getting loan as my primary residence because advantageous for interest and down payment. 

We are getting loan as my primary residence because advantageous for interest and down payment.