There are obviously a lot of moving parts. I don't know your rate or have all the information, but I see options. If you have been in the loan for a while, you may be able to do a rate/term refinance to lower your payment. Even if the rate is higher, by refinancing you will extend out the 30 year term by starting a brand new 30 year loan thus giving you more cash flow. I would do this now before you move out so that it can be considered a primary residence and as long as you have consistent income (once you leave your job that can be a problem for a lender).
You can also do a cash out refinance on your current SFR (though the rate would be higher) in order to utilize the money for a down payment. You typically can only cash out up to 80%, but you can likely get a HELOC up to 90% or even higher to allow you to buy the new co-op in cash.
From a cashflow perspective, one way to maximize cash flow in NYC is to use Roomeze.com. Instead of renting out the whole house, they match up roommates to sign a lease together. Each person pays by by bedroom, which will yield a higher return than if you rent out the whole house to one tenant, but won't be as much work as doing an airBnB.
The way I see it (depending on what your property taxes are) there are a lot of options here. I would schedule a time to speak to your lender to go over your options as I am sure there are options I am not mentioning here. If you don't have one, I'd be happy to speak to you. I see no reason why you can't keep your current property and buy your next residence in cash. Just make sure to keep in mind that the co-op will still have maintenance fees and depending on how financially sound the building is large assessments or increased maintenance costs can be a consistent increase in cost that's out of your control.
Good luck! I hope you have the opportunity to chase your passion!