Simplify switch network for dual-element heater

I have a small space heater that each has a pair of quartz radiant heating elements. Each element is 400 Watts with individual latching button switches. This allows the heater to operate at 400W or 800W (either of one button pressed or both buttons pressed).

I find that the heater is often too hot and I'd like to add a 3rd option of 200W. This is accomplished by placing the two heating elements in series across the incoming line.

The ideal situation would still use only two button switches with the heater power selected in binary fashion. Two buttons gives 4 distinct states: Off, Low (200W), Medium (400W), High (800W).

The existing button switches are SPST and appear to be rated at 10A or so.

I've been doodling and the best arrangement that I can come up with requires replacing one of the button switches with a DPDT version. I'm having a real problem finding a suitable switch.

I'm hoping that someone can suggest a better alternative to what I have so far:

simulate this circuit – Schematic created using CircuitLab

The 4 combinations of SW1 & SW2 allow for heat selection of: Off, Low, Med, High.

What I'd like is suggestions of how to simplify this to, perhaps, two SPDT switches instead.

Worst case scenario is that I add a beefy DPDT relay controlled by the existing SPST SW2.

• +1 for the interesting question. I think it's impossible with only 2 SPDT, but only because I've failed repeatedly. I wonder if there's a Bridges of Königsberg type proof for its impossibility? You could try this question on the mathematics stack. If it helps, I can switch a heater between 4 heat settings with only 2 SPST, but none of those settings are 'off'. Nov 26, 2017 at 4:29