I got the stain on yesterday. It is starting to look better.
The area around the edge looks a bit splotchy but that's because it is going to painted black instead of stained.
The only part that did not come out so well is where I burned through the finish. That wood didn't take the stain at all.
I tried using a wood stain marker also to no avail. I think I'll sleep on it one more day and see if I can come up with something to darken that area.