Sorry for the delay, had a few other things to wrap up.
I created your simple 2-bone armature and rotated one bone through 180 deg in a single axis using 3 keyframes @ 0f, 51f and 101f. I then exported to .fbx using the binary option (Blender cannot read back the ASCII format option).
You are correct, unchecking Baked Animation disables all animation export – that’s not an option it’s an off switch! Seems like a poor design choice to me but there may be a good reason I don’t know of.
In any case, when the Baked Animation is enabled, keys for every frame are exported but ONLY if you leave the Sampling Rate at 1. This parameter determines the frame-count “step” between exported keyframes. This is not ideal because keyframes in Blender are rarely set in specific frame intervals, except perhaps in test files like mine. However, this setting can be used to limit the number of keys exported, making subsequent editing a bit less cumbersome. Not ideal but it’s what can be done. In my test a Sampling Rate of 50 reproduced my original keyframes when I imported the .fbx export back into Blender.
Hope this is useful.