The neck is glued in and I filled the gaps with wood filler. After drying and sanding, I applied Minwax Pre-Stain.
Never used this product before, but it seems to give a nice even surface (that's what it's obviously for, d'oh!). However, I'm not sure how well the stainable wood filler will work with the actual stains. It's also Minwax brand, so I HOPE it will work. Right now, it's sticking out too much for my taste. BUT, that stuff has warning labels all over it and it smells very bad. All windows open, dogs can't get in until in the evening.... Not sure I'm gonna use that again.

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