What would the timing of initiating a 1031 look like? 

I would have the seller initial or sign something acknowledging your disclosure of agent status. 

I initially wanted to put this equity to work via HELOC or cash-out refi, but I'll just skip to the part where I've decided that I will sell my primary FSBO directly through a title company.

Good point @Stephanie P - "The new loan amount can be no more than the actual documented amount of the borrower's initial investment in purchasing the property plus the financing of closing costs, prepaid fees, and points on the new mortgage loan (subject to the maximum LTV, CLTV, and HCLTV ratios for the cash-out transaction based on the current appraised value)." 

All I have is LLC initial and phone number of person whose real name I came to know from somewhere else.Please help.

Initially, I was thinking that I would like to purchase a small multifamily in the greater Phoenix area.

✍️Role of a SyndicatorThe sponsor/syndicator is the person who initiates the real estate syndication; they are responsible for identifying the market, underwriting the property, securing financing, overseeing the business plan/renovations and the daily activity of the property management company, ensuring strong investor relations, and managing the asset in general.

Below are my initial thoughts: 1.

Did you imply that if the property was initially my primary residence, then the 2/5 rule will apply?

Upon inspection of the apartment that initially reported the mouse issue, the apartment was in the same condition it was a month ago.