I have a few things to add. For some context, I've been building software for 22 years, have ran my own company, and worn many hats. The thoughts below are also in the context of hiring senior people.
Moving fast and being responsive is really important, i.e. be lucky. I only just this week moved from part time consulting to a full time job. I think I was very lucky, but from the first moment of contacting recruiters/applying/reaching out it took only 1.5 weeks to get an offer that exceeded my expectations. It is hard to be lucky enough to capture the attention of the right application at the right time.
Include the salary in the job ad. I only applied for jobs with salary in the ad. It saves everyone so much time to know that everyone is in the same ballpark before starting any discussions.
Look beyond the resume. The trouble is over 20 years, I've done A LOT. So many different technologies, problems, industries, roles. It's too much to condense into a resume that perfectly fits your expectations. Come up with some probing questions that are relevant to what you need from a problem solving point of view, and ask those. I remember interviewing and it prompted a whole set of memories I had omitted from my resume and cover letters, all because I just plain forgot.
Be proactive. For example, I added a post to a monthly "whos looking for work" post on HN. I didn't hear from you and I would have loved to. Maybe I wasn't the perfect fit, but no way to know unless we talked. I wonder how many other potentials could have been missed?
I wouldn't worry about whether or not the take home technical assignment is causing issues or not. You will need some way of evaluation candidates in a practical way, and it might be video discussions, or it might be take home assessments, or something else. All a quite time consuming, and will exclude people who don't have that time. If people are genuinely looking and are interesting in your team, they will find a way to make the time. Perhaps be flexible in this point and work with the candidate to decide what method of evaluation works for both parties.
I don't pretend that the above will fix any hiring issues, but I think it's worth considering. In a job market where there is an overwhelming demand for senior people, ask yourself - why should they work for you?