The thermocouple and associated hold-in solenoid in the flame failure device work at surprisingly high current (for a single thermocouple anyway) - 10s of mA, but VERY low emf, a few mV at most, hence the solid copper construction of the 'lead' between them, it's a very low impedance circuit, the solenoid is a few turns of quite thick wire. It's very unlikely that you would be able to break in to it and hook up several thermocouples in parallel without adding excessive resistance and losing all your emf in the process.
More importantly you need to consider that the flame failure device is definitely a safety item and you really shouldn't mess with it. Series connecting several thermocouples could well delay the gas shutoff by far too long. You could maybe try re-positioning it a bit closer to the flame, but it sounds as if it's serving its function - guarding against a flame that's in danger of blowing out.
This. It was not part of the original burner, but added later as a mandatory safety feature (the company runs 'events' and these gas burners are part of the show, someone is always on site with them). You also highlighted what I suspected... very low output voltage (~25mV) driving a very low resistance solenoid (<1ohm). This also makes adding a tilt switch troublesome as mercury free ones tend to have >1 ohm resistance. With that said I'm fairly sure there are larger tilt switches that use microswitches and a 'weight' rated for @3A @ 125VAC that should have minimum voltage drop.
I agree that one should leave this system in place, perhaps with an industrial tilt switch in series, as its directly controlling the valve with no extra electronics to go wrong (failure from low battery, connector corrosion etc..). However, if we simply cannot get the thermocouple close enough to the flame for reliable operation, I fear I may have to use active circuitry, and that is where I'll have to be clever about it.
Simply measuring the voltage of several thermocouples and controlling the valve output is one way, but even driving the solenoid will be inefficient (30mV @ say, 30mA?) unless I use the thermocouples power, to power the solenoid. With several thermocouples connected to the drains of MOSFETs, that all have their sources commoned: a magnitude selector, that connects the thermocouple with the highest output to the solenoid. I suppose in effect, groups of ideal diodes. Would have to have a make-before-break selection, with rather tight timing because a break would trip the valve closed, and a sudden addition of another thermo (whose output is just starting to overtake the previous highest) connected in parallel would also cause a minor glitch..
It would of course still need a power supply, and a rather high voltage (>5V) one to make sure the FET's are fully turned on, and to keep their on-resistance down, but as the switching will be very low duty (hopefully) the actual power consumption could be low - at least as far as driving the switches is concerned. Comparator circuits would still draw a few mA so a PP3 would probably get ~100 hours out of it. Whilst its cool, its probably wise to not power this with a solar cell and a rechargeable batt.
The above idea is pretty much the 'worst case' scenario. I'm hoping to see the actual burner at the weekend, and try to convince the owner do drill a hole in the basin for the thermo, negating all of this.
Cheers for the help!