I'm also an indie dev. My take on your questions:

- Look at their portfolios, make judgment calls about which ones do the best work, narrow it down to a short list. I would then have a brief chat/exchange with the short list members to try to learn a bit about their process. My goal here is to evaluate whether I think this person is thoughtful about what they are doing, can communicate sufficiently, and can mostly direct themselves. (If I knew exactly what I wanted I wouldn't be hiring a designer.) After this, if you want to be extra cautious, you could ask for a few references. But for your budget, if the previous steps check out I would probably just skip that step.

- I think your approach of posting a job for bidding is probably not best although I haven't tried this myself and not familiar with that subreddit. You want to pre-select the quality designers who are likely in demand already.

- Your budget is pretty low for all the items you listed. At that price range for all the things you want, you're probably going to be limiting yourself to people who can't improve what you currently have in a major way without direction from you.

- My approach when I tried this recently was to go on dribbble, check out shots of the thing I was looking for (in my case logos - in your case landing pages), and make a list of great designers who had a lot of examples of what I wanted.

Some more feedback:

- Why change the logo? What you have right now is great A+.

- Fonts and color scheme are not great but probably not that important right now.

- If you hire a designer, focus on someone who specifically has experience building great landing pages.

- The problem with your landing page is the visual clarity and messaging of explaining the value prop to the user. Right now it's somewhat visually overwhelming due to lots of text, moving things, poor job of creating contrast between sections and call outs. I'm not sure where my eyes should look when I hit the page. Copy, ie the wording, could improve also.

- Design is not as hard as you think. You can probably get 75% as good a the result as a pro designer by spending two afternoons studying examples of other well designed landing pages and paying attention to details of what they did, then applying it yourself. You will learn a lot in the process too.

HTH, feel free to ping me at hnusername[0:4] @ u [windy city] edu.

Having looked at the site, if it's not successful enough to justify paying a great deal more than $1000 for branding and redesign, then it's not worth putting effort into managing a branding and redesign at the cost of making it successful enough where $20,000 isn't an issue. In other words, does it already look good enough that appearance is unlikely to be affecting growth among the demographic likely to use it?

Redesign of the website should be based on good user analytics and the people who can do that well are expensive relative to fiver and other find-the-low-bidder sites. They're expensive because they're busy with clients who can pay well.

Good luck.

Hmmm, I'm worried that you're right. But $20,000 is at least 10 times what I'm comfortable spending at this stage.

Is there no option in between fiverr and $20K that would be a worthwhile investment?

My question is: what evidence did you use to determine that the design of the website is the bottleneck for growth?

If it's not the bottleneck, then $10 is too much.

To get sound evidence that the design is the bottle neck the expertise for such determination is probably an order of magnitude more than you are looking to spend.