If the metric size is M8, then 5/16 is my guess too as it's 7.9375 mm, ie very close.
UNC also makes sense for this application, 18 tpi. Same size UNF is 24 tpi.
I've got and suggest one is useful to a Morgan owner, a thread gauge. Sort of thing you ought to be able to buy cheaply from an autojumble, but I was given mine!
