You're overcomplicating it; you only need a single clutch and in/out springs[1] to do this. If you're spinning at 4000 rpm and your springs cover 6 degrees of rotation, then your clutch needs to be able to actuate at 4000 Hz.
When the clutch is engaged, the engine-side springs compress to supply the torque and match the speed difference. When it's disengaged, the springs expand back out as it returns to engine speed. The obvious problem is that clutches do not smoothly click on and off like a transistor.
However there are more specialized devices that use stick-slip dynamics like piezo actuators. Since there is a much more rapid transition between "on"/"off", they can be very efficient and allow relatively weak devices to exert very large forces. They're just only able to take very small steps.
> When it's disengaged, the springs expand back out as it returns to engine speed.
What is it?
I think you need an intermediate flywheel, with springs and clutches on each side. The intermediate flywheel's mass is tiny, so might be formed by just the masses of the springs and clutch mechanism.
It is the clutch. The clutch is your flywheel; it's free floating and connected to the driveshaft with springs. When its engaged, it is connected to both shafts by springs. When it's disconnected it's only connected to the driveshaft by springs.
When the clutch is engaged, the engine-side springs compress to supply the torque and match the speed difference. When it's disengaged, the springs expand back out as it returns to engine speed. The obvious problem is that clutches do not smoothly click on and off like a transistor.
However there are more specialized devices that use stick-slip dynamics like piezo actuators. Since there is a much more rapid transition between "on"/"off", they can be very efficient and allow relatively weak devices to exert very large forces. They're just only able to take very small steps.
[1] Labeled 4 here: https://haynes.com/en-gb/sites/default/files/styles/blog_lan...