I just wanted to say, I stumbled upon your website a few years ago through the Tromp-Taylor rules of Go and found the things you do impressive and inspiring. It’s a nice surprise to see you commenting here.
So to summarize, the game tree complexity is estimated by estimating the branching factor and the game length, and raising the former to the power of the latter.
I find it slightly odd that the game length is calibrated to "reasonable" games but the branching factor is not.
If the goal is to estimate the number of possible games of go, then the calculation would be dominated by the number of long games rather than the number of short games, and very long games are possible.
If the goal is to estimate the number of "reasonable" games of go, then the branching factor should also be much smaller, as most possible moves are not reasonable. Perhaps the logarithm of the branching factor could be estimated as the entropy of some policy model such at that of KataGo.
P.S. I am happy to have received a reply from the mighty Tromp!
We discuss the numbers for Go in the introduction of our paper https://matthieuw.github.io/go-games-number/AGoogolplexOfGoG...