I agree totally, that wheelbarrow timing is a very interesting problem. The solution is highly variable, even leaving villager vs army considerations.
I try to judge this way: Wheelbarrow as we know takes same amount of time as 3 villagers. So, the question is, if the 3 future villagers add to the economy more than the boost that wheelbarrow technology generates for the whole economy. If we have one lumbercamp with 8 villagers working on it, and it is not viable to add a second one in a separate forest due to strategical/tactical reasons- then we know that we would end up adding 3 relatively ineffcient vils to wood, or lets say 2 vils to wood and 1 to a relatively far new farm. In this case, getting wheelbarrow would be a great thing.
On the other hand, if you have 2 lumbers, and can add more vils to wood without much loss of efficiency/you have good farming spots left for new farms that are close enough to dropsite, you can delay getting wheelbarrow since these vils work efficient enough.
And I think this is the exact situation many times if you go relatively fast castle around 19-22 mins, or even later, you have quite efficient (or enough effective) economy, with less than 20-23 farmers. So far I rather chose making 3 more villagers in this case until castle age with more farms.