It sounds like a great idea and I hope it works well for you!
Not hoping to be a negative nancy, but that was not an option for me at all. I did not (and still do not) find having enough money to literally say FU to be sufficient to throw off the chains of social pressure and our ambition-culture. In many jobs and careers, part of being good at your job or doing a good job is working yourself nearly to death, not just the quality of the work you do. So as much as I would like to have been able to leverage my FI status as a lawyer to say, "I will only bill 1000 hours this year"....it wasn't going to happen. This is actually a possible negotiation one could have with certain firms, and of course if you were a sole practitioner (or partner) you could make certain choices, within certain parameters, on your own. BUT, the part that I knew myself well enough to know I could not do, is to feel like I was doing a good job part-time when the whole underlying, subconscious definition of doing a good job is basically working ALL of the time. There are exceptions for certain semi-retired lawyers who put in 40 or more years and are starting a slow decade of working fewer hours in hopes of not dying literally at their desks, but otherwise, part of being a lawyer is being available all the time. And I am not sure of the value of working only 20 hours per week (or even 40!) if those hours still might have to be on Sunday when I was supposed to be at my friend's wedding or at 3am or what-have-you.
So, I think the problem is the illusion of control with FI rather than real control. With some jobs/careers you could have real control and FI could meaningfully change your life and the way you work. But not so with others. At my firm, let's face it, all of us could be or should be FI given how much money we made. But, it's the culture that doesn't allow that kind of control of your time and life. And I couldn't change the culture, so I left it.
I think your plan is good, to try it out for 3 years. Certainly a low-risk, easy to implement plan that will be interesting to learn from!