Grant, it sound like a "Push Drill" to me, particularly since the bits
have two straight flutes as was then the common design.
At a glance, the tool iself looks like the classic Yankee Screwdrive,
and employs a very similar rotation mechanism. I believe that Yankee
may have even manufactured push drills as well as screwdrivers. The
push drills were much faster to use than the conventional variety of
hand-cranked screw drivers that were still the major alternative.
Both of these tools pretty much vanished from the market after battery
operated drill/screwdrives made an appearance, but through the late
1950s both were found in most cabinet makers and carpenters tool boxes.
They were particularly popular with storm window and door contractors,
because they needed only one hand to operate, freeing the other to hold
the storm window or door fram in place.