A slightly extended thought

The main antagonism here is that the hiring company wants to minimise its effort in getting great devs, and the devs want to minimise their effort in getting great jobs.

The first point to note is that constant marketing is the first, best solution to this. I would definitely put more effort into joining a well-marketed company (StackOverflow?) than J.Random Inc. So both me and J.Random Inc had better put some effort into standing out from the crowd.

OSS is one seemingly good way to do this - and having a reasonable Github account is something I would say should get you through most interview filters (ie if you are looking for a Python dev, and they have commits to say a flask extension or bits of salt-stack, then you can blip over the Fizzbuzz and whiteboards.)

But marketing is simply a way to get past other people's filters. "Networking" is good, whatever that might mean, and being a good citizen works. but these are as always, long term, constant application efforts. And of course, costly.

Secondly get over the "we only hire the best of the best of the best". If that's true then like the SEALs you clearly have a six month training programme that takes the best and shapes them into effective teams, fully paid while they learn - yes? And the training staff for this programme are pulled off current fee-paying projects to keep up the standards yes?
Otherwise your best-of-the-best is so much auto-trumpet blowing. So please leave that at home. Focus on process not heroes.

The interview by takehome project is a big problem.

Yes it clearly weeds out candidates - mostly by making the ones with options elsewhere go elsewhere. (Even Google, with its firehose of applicants, seemed to realise this was a dumb idea and instead used the MIT graduate program as a filter instead).

My main issue with interviews-by-homework is it is usually a hole-dig-and-fill session as the problem has been done by dozens of people before (often you can find their solutions on github). My time is then valued at less than zero. As a filter before we get to interview, it really is just an artifical hurdle. All you are saying is that "we have soooo much choice we can make you dance before talking to you" - if it works for you great. Your marketing is working (see above)

IMO a better approach is to find different existing properties that you can filter to get applicants to the interview.

Sometimes these are "Alpha Male" filters like 1st class honours at MIT. Other people on HN stand by different filters - I seem to remember someone saying one of their best hires had taught themselves coding whilst getting off drugs in a Glasgow slum. How you filter for that is harder than the MIT problem but I bet its a less tapped seam than MIT.

Overall, a good interview process is probably focusing on the wrong end of the problem. If you have a new open position and then you start looking its too late. Be a good OSS citizen, be involved in the community of developers (OSS and elsewhere), find ways to reach out to unusual developers, or people not marketing themselves, and keep the process going constantly, with suitable investment. The general Big Co idea of "you cannot put out job ads before you have a signed off budget and position" tends to make this a problem. A solution would be to take the expected Agency percentages for each new hire (between 5-20%) and put it into a centralised "developer evangelist" team that just gets people through the door.

This way when you need to open a new position, you will have four people in mind you already want to hire, and you can just go to Starbucks for an interview.