An alternative to knowing the carabiner size precisely would be to select a range of extra length to get in the ballpark, then precalibrate by touching off on a circle of known size. Perhaps a circuit board taped to the spoilboard could be the precise circle. A 555 circuit and 2032 battery on the circuit board produce a signal that goes away when the touch probe leaves the circle.
The touch probe could be a length of straight wire, or standard pogo pin inserted into a router collet.