> Why did the wagon the rails/logs were laid for have the outside 5'gauge?

At this remove in time, this probably can't be definitively determined. Most likely it was the "gauge" of the wagons in use by the Newcastle-upon-Tyne operation, and all Beaumont did was built a "supported duo-rail fixed guideway", base on those mine cart log-rail tramways, without resorting to the additional expenses of redesigning and rebuilding the wagons too.

>Was this the standard for wagons of the era and, if it was, why?

1): possibly a standard of sorts, at least in England, and 2): don't know.

The reason I put a fair amount of credence in the narrative is because the author was almost contemporaneous with Stephenson and probably had access to several first-hand accounts.