A little more fodder for your sanding protocol thought process. The dust created while sanding will fill every little fingerprint and crevice on your hands. If you sand and then run your hand over a surface it will feel "really" smooth. Now without doing anything else, wipe or wash your hands and blow or vacuum the surface clean; now run your hand over it and see how it feels.
I find that being consistent in sanding every surface I am after, blowing off the spoil and then moving to the next grit and again, be very consistent to go over every area . . . .rinse and repeat . . . gets me the surface I am after quicker and with less follow up or touch up. When it comes to sanding it may seem like you are taking longer to be doggedly thorough but, in the long run you are saving time.
The coloring in the wood you have is really attractive.
If it is cottonwood, the grain is typically very interwoven and not straight, which means it is not very stable. Boards tend to twist after milling. How much that would affect what you have may be different since you have smaller chunks.
The cottonwood here in Montana tends to be a softer wood, definitely not hard like maple.
I'm here today because a boy sent over to VN managed to come home. He came to one of my classes one day to present on patriotism. He brought a photo album that had a post it note on every photo that had a person in it who did not come home. There were no pages free of post it notes.