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Nice Idea but any safety concerns? Wood in direct contact with the Weber. Maybe create an air gap between the grill and the table top and suspend the grill in a fire safe way.
A word of Warning. A metal insert will through metal chips upon the initial cut through it but may also periodically throw metal chips if the arbor has even just a small amount of play in it. I just made an aluminum insert and I'm a little conserned about the safety aspect.
Hum...If using min and max values, how about instead of subtracting 516 counts as an offset, consider:RMScurrent = (maxCurrent - minCurrent)/2.0 *0.707 / (your constant)
Since the output of the current transformer is AC, doesn't the output (after the shunt resistor) need to be rectified and smoothed. No need to bias such a circuit so long as the common of the rectified signal is common the the Arduino's analog ground. Hardware signal scaling would be accomplished via the shunt resistor value.
Was Googling around for baluns and found your Instructable. You may want to double check the transformer schematic. On the 300 ohm side where the two windings #2 & #3 connect, I think that net should float, not connect back to the 75 ohm ground. As it is shown currently, winding #2 is shorted.
Neat Project. For the watch strap... There are some one piece nylon watch straps out there. I found a few on Amazon but they are 18-22mm wide typically. Could modify PCB for a std. one piece strap for a highly finished look. Just need to weave the strap through the two slots in the PCB.