I've been working 4 day workweeks for well over a decade now, took the pay cut myself.
As for the goal to maintain 100% productivity whilst cutting back on hours, I'm confident that they will succeed. In fact, they'll succeed in this without requiring some kind of brilliant plan, as this recalibration happens automatically.
When you start working one day less, nobody will reduce your workload by 20%. You'll have the exact same workload as before and now need to achieve it in less time.
There's many ways to cross this gap. An obvious one is that a typical 5 day work week has moments of slack, depending on the culture. Friday after lunch is where productivity sinks in many offices. Wednesdays are also slower as it's typically the first moment in the week where things are running (planned, prepared, on track). In a 4 day work week you sacrifice this breathing room, the 4 days become more compressed.
Another natural change is to take a more aggressive stand in rejecting non-sense. Excess meetings, unimportant emails, etc. This works very well and is extremely effective for the simple reason that you MUST. As such this time compression is a blessing, a cleansing mechanism for yourself and the organization.
You'll be amazed at how much time you can win back. Let's say you do need to attend a meeting. It's a 1 hour meeting. You're needed in the meeting. Go in and say you only have 20 mins. As if by sheer magic, what needed to be discussed gets done in 20 mins. Without this forced "budgeting", people would just fill the hour with bullshit.
Counter intuitive, but by being rigid instead of elastic, you maximize value.