Charge the tenants a higher rent rate and include utilities with their rent.

You have to include the cost of your time and the work, especially on a "scary house" is daunting indeed. 

House hacking is a financial no-brainer, it eliminates you single biggest monthly expense, so you can increase your savings rate.

As of today, the house rents for $3,400 per month and my PITI is $2,500 per month.

There isn't enough information in here about the current state of the house to be able to advise you, but I would think #3 is a definite no as it seems unnecessary from a cost perspective although that market has scale to accept it.

"But rates have been at 7% or higher in the past, and investors still did well!"

After 20 years as an investor, broker, and lender, I can tell you that house hacking is one of the smartest ways to start.

You have to put 5% down vs 3.5% down, rates are usually higher, but if you have strong credit, your PMI cost can be cheaper than that of FHA loans. 

My plan is to sell my primary home in New York and purchase a house to live in South Carolina.

It's debt you'd still have to pay back, but at least you will not touch one of those two amazing interest rates.