Hand Tools Archive
can't comment on what was historically done, but I would look to common planes to guess what was used, and the coffin smoother works just as well as a stanley for fitting and working small areas. At least in relative comparison.
When you get into much harder woods, it gets easier to do faster work with a metal plane, but for typical drawer materials (pine, poplar, soft maple, chestnut, etc) I can't imagine any issue with a coffin smoother.
Since your latest drawers are ash with grain going all over the place, I think most people would do better with adjustment and cap iron set with a stanley for that.