The problem is that conventional lenders don't like wholesale dealings. 

Great idea@Nathan -It's NYC  - a tenant favoured state, and the building has no conventional  mortgage 

Prices have started to climb due to the lack of inventory.

Hi thereI just became a 1099 and I am not eligible for a loan for a while, regardless of my current assets in retirements funds. How do you find hard money lenders?What are my other options? Family/friends isn't an op...

I received a message from a buyer who has conventional financing and is interested.

If there's inventory the 1031 won't cause you added heartburn. 

I have enough to buy the second all cash (just sitting in a 1.6% ally bank account at the moment) but i'm wondering if I should leverage my money and try and get a conventional loan or possible some kind of HELOC on the value of the first rental.

No cash back on owner occupied only investor loan.I have built homes and some rentals in years past and owned rental properties all through bank or conventional financing. 

I also agree with @Lee Ripma that a small multifamily can be even more lucrative since you can gain more in rent, but affordable inventory of 2-4plexes in desirable areas in KC seems to be low right now, which makes it tough to find a deal.

Are you planning to get a conventional mortgage or a hard-money loan?