Which furnace valves are you thinking of using? Are you going to be PID controlling some of your burners? Did you find furnace valves that operate with high pressure propane or did you mean to write low pressure?
My set-up uses the honeywell vr8200 valves and I have to manually press and hold a pilot button on the valve while lighting each burner. These valves have the pilot and thermocouple (which senses if the pilot blows out) built right in. This takes 30 seconds to light all the pilot lights. The standing pilot light makes the rest of the set-up so easy.
Assuming you are going to use PIDs for temp control:
With your idea of the grill push button, what would you use to ensure that the grill lighter fires at the same time the gas turns on each time it cycles on/off?
They make fancy electronic ignitions, but I was under the impression that they are a bit spendy.
Never underestimate how much assistance, how much satisfaction, how much comfort, how much soul and transcendence there might be in a well-made taco and a cold bottle of beer.