Low acquisition price, medium investment cost.

Not only that but you are going to carry a Heloc in a 2nd lien position and you will not be able to pull out more cash unless you do a cash out refinance to pay off the previous Heloc and take out more cash.85% of the home owners who take out a Heloc refinance in 3-5 years so it makes more sense to simply do a COR and avoid the future closing costs.

The total cost of project is more than we can qualify for based on personal income, although our W2 income and credit score all work in our favor.

I self manage 4 properties on my own and I don't think there is that much paperwork associated to bring in the cost of a VA. 

Unless you know NJ landlord/tenant laws along with the commercial side of it, it may cost you more money NOT to hire professional management. 

Construction lenders will look at the total cost and typically finance 75-80% of the project (right now its more difficult to reach the 80% threshold with market uncertainty).

Can I expense my moving costs if I am moving across the country to pursue RE investing full-time in another state?

It's dangerous, deadly and costly.

We then need about $30,000 to cover the hard money loan and the closing costs.

They don't cost much and give you protection.