Transconductance is a small signal parameter, and not really suitable for estimating behavior in a switching circuit. I've never seen a method based on transconductance. From what I can tell, that document is suggesting that you use gm to estimate the plateau Vgs, but that's a pretty dubious suggestion IMO, since, as your datasheet suggests, gm is not constant.
It's probably not possible to get exactly the data you want for your exact operating conditions. That's typical for these sort of things. You'll just have to choose an approximation, erring on the side of caution.