Looking good! That sanding sure seems to be a ton of work, but it will be worth it to get the finish you desire. It's nice when you find a good combination of sandpaper and sander. I have found that it doesn't often pay to scrimp on sandpaper. The cheap stuff may look like a good deal, but if it only lasts 1/10th as long as the good stuff, and doesn't work well, that's just not worth it.
Out of curiosity, why did you use birch for the front and back if you're just going to paint it? It would make sense to me if you were painting the front and back, but only lightly, so you still could see the woodgrain. It doesn't appear that's your goal.