With the greatest of respect to you Scott, if you have put money into your idea and your plans, then put money into the design of your app as well. Hiring a designer and paying them out of a budget is the fair and accepted way of doing business. It also happens to be how the rest of the world usually does business. I give you a service, you pay me for it. Your product does well, you recoup the money you paid out.
Unfortunately, many of us designers hear similar things from clients all the time. Here's a list of things that clients (even with the best intentions) say to designers and others in the creative field:
I can't pay you, but my idea will make so much money. I'll give you a share of it if you work for free until then.
This will look great in your portfolio.
It will give you more exposure.
I'll put a link back to you on my website.
We don't make any money on it yet so why should you?
We're just doing this because it's a great idea. We'd love you to be part of it. There's no pay though.
And so forth.
To summarise, edit your post, delete the bit about percentages and instead, welcome quotes from designers who would otherwise be willing to work with you. You don't have to hire me or any of them. You'll still have a few quotes to work with. I'll even give you a quote myself. It might be fun. When you find the average or a particularly good designer that can give you what you want, you'll know that's where you should be aiming to set your budget. You might also want to be more specific about what it is you want designing. Three buttons? Five screens? Sixty maps? A thousand icons?
I have a feeling that you will unfortunately not edit your post with my suggestion and even if you do, won't end up working with anyone on this board due to prices being in three figures instead of two but I do welcome you to prove me wrong on this and I wish you the very best of luck with your app.