Steve,
50-60 years ago, precise measurements were done with steel tapes and a prism. For large events, the officials would take a couple of days and lay out 1-2 flight lines beforehand using a transit. For each flight line, pairs of stakes with lines stretched between them would be precisely positioned every 100 or 200 yards, establishing reference lines that were parallel to the flight line. A 100 yard steel tape was used to measure the position of the arrow relative to the nearest reference line. If there was doubt that the tape wasn't being held square, then a prism would be used to ensure that the measurement was made perpendicular to the reference line. It took more upfront work back then, but it seemed to have work pretty well. The only downside is that once established, the flight lines are not easily moved. I believe this is how the measurements are still done at the UK flight shoots.
Alan