Buck converter for ATTiny power supply?

I see. I looked up some buck converter theory after reading this. Would I be right in saying that the output voltage/current ratio is dependent only on PWM (not on capacitor/inductor values) in a perfect example of this circuit?

The average output power is dependent on the PWM value. Longer duty cycle means current flows for longer time, increasing the overall power dissipated in the spring. If you add the LC filter you stabilise the current/voltage the circuit sees to an extent (how well depends on the values of the inductor and capacitor).

The momentary current/voltage ratio is still dependent on the other circuit parameters, such as the resistance of the spring itself.

In your case, you came with 6.55V on an input of 7.4V (that voltage is of course also not constant over the charge level of your batteries) you'd need a duty cycle of about 89%, which gives an analogWrite() value of 226. This also allows for much easier fine tuning of the power supplied to your springs, you just change that value a bit as needed.