Here are the bottom cracks, for all to see. I decided against filling them, didn't think it would improve the looks.
I did try the white glue method, but the cracks didn't close up. I could only find two 8 oz bottles at Walmart, just enough to fill a quart plastic cottage cheese container along with water. The piece was just small enough to fit.
The next day when I went to take it out, I couldn't budge it out of the container--it was stuck tight! Had to gently pry it out with a butter knife. No damage to the wood, not even a scratch.
Just a slightly flat bottom, nicely balanced overall so that when it's set on it's side, will sometimes right itself up on the base but it does a little dance first!