> 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.
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.