Time for a reality check.
You are asking someone who has at least $150,000 of earning potential to donate an unlimited amount of time and energy for a worthless piece of paper (stock), all pursuing an "idea" that, even under optimal circumstances, will almost certainly fail.
Anyone who agrees to this proposition suffers from impaired judgement or a complete lack of more attractive choices, neither of which bode well for your already-doomed startup.
All sustainable relationships have to be reciprocal. In your proposed scenario, the full-stack engineer of which you speak holds the entire balance of power, because they have the ability to create value by translating their knowledge and skills into working product. Unless you bring more to the table than a worthless idea, a worthless piece of paper, and possibly a worthless title, then you will not be able to create let alone sustain such a relationship.
What do I recommend?
First, look to your network. If you don't already have deep relationships with full-stack engineers -- relationships that establish mutual trust and respect -- then you're almost certainly doomed. On the other hand, if you DO know someone who trusts your business acumen, based on your track record (not necessarily in the same area), then there's hope you can form an alliance.
Most likely, based on the question, you don't have any relationships with full-stack engineers who would trust you enough to accept this risk. In that case, you're almost totally screwed.
I say almost, because you have three remaining choices:
- First, you can raise a seed round. If you can't raise a seed round, then why should any engineer worth her salt trust your business acumen? They shouldn't.
- Second, you can save some money or make enough money that you can compensate a full-stack engineer for her time. Don't look in NYC, look in other countries where the cost of living is much less.
- Third, you can learn to become a full-stack engineer yourself. Programming is not something for rocket scientists, almost anyone can pick it up. If you aren't even willing to devote the time necessary to learn how to implement your idea, why should you expect someone else to be? A benefit of this approach is that you'll learn what it feels like to be on the receiving end: someone with an "idea" wanting you to fork over hundreds of thousands of dollars in exchange for something that's objectively worthless.
I tell you all this not to discourage you, but to present the facts. If you have an idea and are passionate about it, then you can make it happen. But don't expect it will come easy or for free, because it won't.