Developing contacts with other investors may lead to useful information, assistance, and even joint venture prospects.Examine the several financing choices that are available for buying houses, including conventional loans, FHA loans, VA loans (if appropriate), and even portfolio loans from nearby credit unions or banks.You might think about contacting mortgage brokers who focus on investment homes.

It is just rate and terms refi, so we can increase the construction loan amount which will be taken on draws. 

In the case that tenants in all units have just re-signed 1-year leases, can one not use an FHA loan to purchase the property?

There are a lot of details you haven't filled in in this post (which is fine), but you will likely need a key principal to co-sign loan and a contract with an experienced property management company.The key principle will co-sign the loan to help show the net worth and liquidity needed for the underwriting department.  

Assuming you can cover a decent portion of the $60K from the 401K loan, get some sort of loan for the rest.  

Once we fix our side up and move in the property should be worth $200k-$250k (it was very undervalued at time of purchase).Why not take a larger loan initial on the purchase of the first duplex and lower your down payment, use the cash you have for the second purchase.  

Further, how do I demonstrate proof of funds on a HELOC (ie, the equivalent of a pre-approval letter for a loan)?

Conventional loan How did you add value to the deal?

All appliances (washer dryer, refrigerator, dishwasher, stove), paint thru the unitDo you think it's doable for under 15k for labor, material, appliances?  

I was one of the four original investor to raise capitol to get the loan for construction.