How very fascinating!
Beech, thanks to how the trees suppress everything else and try to outcompete each other, usually tend to be quite straight grained, at least as long as the trees are on relatively flat land. The straightness, being relatively closed, and “hard” are often the reasons for beech being common in wooden hand tools. Birch on the other hand …
Looking for American beech (Fagus grandifolia) rated as NHLA/FAS (North American Lumber Association [both faces good]) can be one way to non-problematic wood. It is mostly very straight grained, as it is difficult obtain that grade with other grain directions. The next lower grade, FAS-1, is a very different kettle of fish.
When dimensioning, using a planer and a thicknesser, it is often recommended to alternate the faces exposed to the cutter of the thicknesser, to reduce re-warp. Though a bit tedious, it can be done with hand tools as well.
Another aid to battle re-warp can be to leave the board 1/32 – 1/16 thick, and then finishing dimensioning closer to the joinery process. I like doing this with hand tools.
The purchase head at timber yard has a moisture meter that is in a very different league than mine. It invariably shows moisture contents to be higher than my measurements.
Just a photo of a maple with reaction (tension) wood due to growing on a slope.