My thoughts on the "new" search page
I would have to agree that the "new" search page is a disaster.
My perspective is based on my background.
Starting in 1976, I entered the IT field. For several years I was a computer programer. Next, I became a lead programmer, followed by positions as systems analyst, project leader, project manager. For the last 10+ years I've worked for a large IT organization in the Quality Assurance group, with responsibility for testing the "useability" of web sites for our customers.
What I would like to comment on, is a common problem that I've seen happen over the years when a reasonably good working system is "updated". You basically had two choices when FamilySearch management decided to "update" the previous search page: 1.) you could have decided to make incremental changes to the search page that already worked reasonably well, or 2) you could have decided to make a major overhall of the search page. You obviously choose to make a major overhall, which almost always has a higher risk of failure.
For some insight on the risk of a major overhall, see the WikiPedia article, The Mythical Man-Month at: https://en.wikipedia.org/wiki/The_Mythical_Man-Month. In particular, I would call your attention to section 2.3, The second-system effect. (Of course, you would have to read the actual section from the author's book.)
In my case, having graduated from the University of California, Riverside, with a degree in mathematics, I eventually, after a few years, ended up working in the business sector. I realized, at that time, that while I was technically competent, I did not really understand how my customers used the systems that I maintained on a daily basis. So, I went back to school, took several courses in financial accounting, cost accounting, etc., and eventually earned my MBA.
The key takeaway is that when doing a major overhaul of a system, in this case the search page, you need to "temper" the enthusiasm of the programing staff with the realities of how the everyday user (customer) will interface with the system. A serch page should be intuitive, for both the beginner and the expert. When you find that you have to write "reams" of instructions for how to search, using the new search page, that should be an indication that you have a problem.
Thank you for giving me the opportunity to give you this feedback.