Fortunately these switches range from $1 to $10 so I ordered a few variations of the switch. I have one here that has the same body with a different arm - it is rated at 6Amps 12VDC and the arms are interchangeable so I can do a straight swap!

If this heavier duty switch is good for 6amps and the solenoid pulls 0.8amps I'm thinking a direct 12v+ feed to the solenoid (5A fused) and a neg feed switched direct from this heavier duty micro switch.