Maybe you answered this before, but I missed it. Why not use a latching bi-stable relay. There is a choice of single- coil of two-coil, depending on how you want it to switch. I was surprised the DigiKey price for the Schrack is only $2.50.
The minimum frequency depends on the relay's resistance, inducatance and minimum holding current. You probably already know the resistance and possibly the minimum holding current, the only thing you need to measure is the inductance.
Also use a Shottky diode as it'll reduce the losses and alow the duty to be reduced even further.
I'll be using a latching relay in the next kit after ladybug (PLC & Ethernect).
Cricket (RS485 Thermostat with 2.5 digit LCD)
Here are the relays I plan to use.