The one difficulty with your proposal is posed by stay-at-home mothers (or these days fathers). It is difficult to discern the difference between someone who has dropped out of the labor market in despair and someone who has dropped out to intentionally pursue non-remunerated work (and raising children is definitely work, and very valuable work when done at all well, even though it is not remunerated) without directly surveying them. One solution would be to count people staying out of paid employment to raise their family as working, but that would require revising and reconsidering all the historical data, since I have no idea what corresponds to "full employment" if one counts takes all working-age people as the population, rather than "the labor market" as traditionally defined, and counts those parenting as employed.
To be honest, there are so few stay at home moms, I think it would be statistically insignificant. Mine was one for a few years.