Springs apply a force that increases as they are deformed from their equilibrium form. To compensate for this, old clocks and crossbows use the horological fusee to compensate.
But, in electronics, to compensate for the similarly variable voltage from batteries and especially from supercapacitors, we use buck converters instead. Buck converters periodically dump a pulse high voltage into an inductor, which ramps up current rapidly in response, and then ramps down (perhaps more slowly) when the high voltage is disconnected. The roughly constant but oscillating current through the inductor is used to charge a capacitor, whose voltage oscillates slightly as the current rises above and falls below the current drawn by the load in parallel with it. The voltage on the capacitor is used to control the pulse width.
The mechanical equivalents of inductors and capacitors are springs and masses, but there is a duality; interchanging current and voltage, and inductance and capacitance, you get a new circuit that functions similarly.
In this case the particular analogy I was thinking of was attempting to maintain a constant but smaller force (analogous to voltage). If force is voltage, then velocity must be current, right? Because the thing you multiply force by to get power is velocity. So the component analogous to a resistor would be a dashpot, as expected: velocity proportional to force. The component analogous to an inductor, with the force proportional to the derivative of velocity (acceleration), must be a mass. And so a capacitor must be a spring, with the velocity proportional to the derivative of force, which is to say, the position is proportional to the force. So far, it all checks out.
So periodically we allow velocity to flow briefly from the mainspring to a mass, such as a flywheel, for example through a freewheel clutch mechanism (analogous to a diode). Then we use this flywheel to energize a spring, such as a torsion bar, connected to a load. The torsion bar is maintained at a roughly constant but slightly oscillating torsion as the flywheel is accelerated by the mainspring, then left to slow down under the influence of that torsion bar or whatever. And then we use the total force in that spring to control the duty cycle with which energy is dumped into the flywheel, by applying and removing a brake (a clutch, really, connected to a fixed shaft that cannot rotate) from the driving side of the freewheel.
It's easy to imagine two rotating actuators, one attached to the flywheel and the other attached to the load, whose difference measures the spring force in the torsion bar, like the pointer of a torque wrench. And you could imagine these two things engaging and disengaging the clutch once per revolution. You probably want those revolutions to be pretty slow, like under 1 Hz, to get acceptable clutch life. You could achieve this either with a large flywheel or by gearing down the relative motions of these timing devices.
So this gives you an efficient, if probably unreliable, kind of continuously variable transmission, with a built-in governor that produce a constant output force (torque), regardless of how fast the output is rotating, as long as the input force is equal or greater.
As an alternative feedback mechanism, you could control the duty cycle of the clutch to obtain a constant output velocity rather than a constant output torque, for example using a centrifugal fly-ball governor.
If we run this the other way around, we have a mechanical boost converter instead. In this configuration, the input shaft is allowed to freely spin up a flywheel, which is at times not connected to any load. Periodically, however, a clutch is engaged, connecting the flywheel to a freewheel which winds up a spring. A second freewheel keeps the spring from unwinding while the drive clutch is disengaged.
When the clutch is engaged, the flywheel can decelerate much faster than the input drive, providing much greater force. If the force required is much greater than the force provided by the input, the clutch will be disengaged most of the time, while if it is almost the same, the clutch will be engaged most of the time.
All of these contrivances seem to me perhaps foolish compared to the reality of continuously variable transmissions achieved by existing methods.
In the world of hydraulics, the boost converter is well known in the form of the hydraulic ram; I suspect that pursuing the analogy further is likely to be fruitful.