I would do the FHA loan and then refinance it to a conventional loan after the first or second year and take that equity and put it into another property.

Doing a cash-out refinance with a lender you worked with in the past is literally the easiest thing ever. 

All of this will add up pretty quickly so you want to make sure that you are in a position to move forward instead of finally finding a home and being told you are $5,000 short on being able to close.3) You can look into using the BRRRR strategy.With $36,000 I would say that you will be in the price range of about $100,000 may be a little bit more.I think the BRRRR strategy would be the best option as it allows you to refinance and take your original investment (plus more if possible) and then start the process over again as opposed to having to save up another $36,000 to start over. 

Should I refinance out of an FHA to eliminate PMI (which would save ~$500/month) or get a HELOC so I can use that capital to invest.

I will continue to live in my duplex due to the WHEDA requirement and hope to refinance into another loan in the next couple years so that I can rent out both units. 

Refinance & Repair:You could refinance the property and use the cash to take care of of the major capex items coming in the near future.

What would I need to propose to a new individual to bring into the deal as a guarantor during a refinance?

If you can get your rehab done quickly, prices are unlikely to change significantly and once you're refinance is complete you are set.

My loan officer needs a seasoning period of 6 months before I can get a rehab refinance loan  Do you know how to get a rehab refi loan on a “new purchase” in the Triad NC?

You can potentially do a cashout refinance and cash them out.