UX freelancer, app/web developer, design thinker
I can answer this from the perspective of a UX designer who is working on a couple startups.
First of all, your second hypothesis doesn't sound feasible. You aren't going to attract top talent if you can't afford to pay them. And you don't want to be worrying about spending your savings at the same time you're trying to get this off the ground.
I'm a bit intrigued by why you absolutely need a top UX designer. As a designer myself, I think that only another designer could be so certain that their specific design is going to be the ultimate differentiator - so good that it could turn into a profitable business.
Generally, a non-designer (most people, like yourself) have a business problem that they are trying to solve. Good design certainly helps, but not nearly as much as actually solving the problem. Your design only needs to be good enough to get customers. Normally it should be treated like any other part of the business else that improves over time (or not) with each future investment.
If you want to recruit someone by offering them equity, you have to sell them on your vision. Attend local events and talk to everyone you can. Tell them your idea and what kind of person you are looking for. (Tip: If you don't want to tell them your whole idea, tell them part of it in such a way that it comes across as the full idea.) If you believe in your vision strongly enough, you will find a UX designer out there who might see your project as the perfect opportunity to make it into a profitable business by leveraging their skillset.
Personally, when I see a great business plan and product that had a lot of potential, and recognize that UX is the bottleneck, I can't help myself but want to make it better.
I hope that helps. If I knew more about your business and product, I could offer more specific advice - even about the interface itself. Feel free to set up a call :)