For context, let me first answer a question raised by RoboKaren in one of the comments:
Once you have three or four applications filed at different types of schools (research university vs. small liberal arts college; different types of departments) I am unclear why it would continue to take more than 3-4 hours per application to tailor.
This is probably true in the US, but in Europe, where OP is apparently also applying, universities often have weird standard CV layouts to use (see bottom of the page) or specific templates for all application material.
The rest of my answer really only relates to applying in Europe. I think for the US, you should be able to just send your standard package anyway.
What strategy could you propose to reduce the time while maintaining the quality?
If you have gone through this process already, what was your personal way of reducing the application effort?
I have gone through the process, and I don't think there is a silver bullet. In reality, I have, for every application, made a conscious decision of whether my predicted chances or my preferences for this position warrant spending however time I expected to need. That is, if they university used a sane, standard application process, I would apply to everything where I saw a sliver of hope or which I thought I might like even a little bit. Conversely, in the few cases where I thought I would need to basically re-write the material from ground up, I generally decided not just to apply.
That being said, a full week absolutely seems excessive just for adapting your material. The most I was ever willing to spend was one or two days per application for reformatting / rewriting (not taking into account when I originally put together my application package). Obviously, we can't remotely tell what you are doing wrong, but maybe you are focusing on the wrong things here? My basic principle has always been that these formatting requirements usually come from administrators who are not deeply involved in the actual decision making process, so as long as you are not obviously violating explicit rules (e.g., if they ask for a 5-page CV, don't send them 18 pages), I have always taken a lot of liberty in interpreting the rules so that it fitted my standard package as closely as possible.
As for how long different stages took:
adapting the cover letter,
About 1 hour. The cover letter was usually fairly geared towards the university, but it needs to be short anyway. And in reality, after a few applications, I had a number of standard phrases that I mixed and matched as suitable.
adapting the CV,
Between 0 and 1 day.
adapting the teaching statement
About 2 hours. My general teaching statement remained the same, but I usually looked through their current curricula to figure out how to best position my teaching.
adapting the research statement,
About 2 hours. My general research statement remained the same as well, but I tried to familiarize myself with the relevant faculty at the institution and I had a dedicated section that explained potential for collaboration that I sw.
adapting the publication list,
Was part of my CV, nothing to adapt.
filling the forms on the Web page of the prospective employer,
Very much depends on the position, but even in the worst cases this should not be more than an hour or two.
getting informed about the prospective employer,
This really is the most time-consuming part, as university web pages are often horrific, and this part I think actually matters to some people on the hiring committees.
asking questions via e-mail or phone and receiving answers regarding the advertised position,
0 hours. I know some people are big on getting in touch with the committee in advance, but I never did it and my personal impression from observing people who do it regularly is that it gives you little new information and no competitive advantage. The story is different if you know a person in the committee well personally, but I am assuming this is not what you mean here.
requesting reference letters,
0 hours. I told my references I am on the job market and they should not be surprised if requests come in. For the positions that require you to upload the letters yourself (yes, those exist in Europe), I had generic versions of the letters available.
I have to apply a lot (200+ applications) and widely to get a chance of, say, 50%.
If you do the math, you will learn that it is unlikely that you will actually be applying to 200+ positions. Frankly, if your scope is Germany, Austria, Switzerland, UK, Canada, and the US, you are not going to find 200 suitable positions to apply to. I am all for not putting too many eggs into one basket, but you probably need to be realistic here. Your field may be small and competitive, but other fields are also competitive, and if you are currently working in a different field and you yourself judge yourself to be a somewhat middling candidate and you are unwilling to spend any time on your application package, your chances are so low that you should evaluate alternatives.
I would propose that you write serious applications for the, say, 30 to 50 most suitable positions you can find, and then figure out what to do if none of them pans out.