Ed wrote: "The circles with the small center dots look like they were
made with a Forstner bit." 

I don't think so.  Those, in my opinion, came from a center-bit.  I've
seen a number of oldsters like these, and center-bits were the go to of
the day.  The oldest I've seen is not a stone box, but a photo of the
excavation for a patch box in the surviving 1803 rifle from the Lewis
and Clark expedition.  

When I was actively researching tools and practices of carpentry for
Sutter's Fort back in the '80s (had to document every tool I brought
there to no later than 1845) I looked at a number of boxed stones for
that period.  Most were not hinged, and the bottom and tops were both
excavated so they could be used just like Sott recommends.  Many were
strictly utilitarian, but a number were fancier; their tops appeared to
have been made out of sections of wide stair rail.  Provides an easy
handle for lifting the top.  Those that were hinged were hinged like
Scott's lovely examples. 

Mike in Woodland