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I always have problems getting perfect mitres. Google Timbermate Wood filler. It smells horrible but is great for those gaps and can be sanded and stained.
Just a note about that glue Titebond III. I have used it for years and it's all I'll use. However in the beginning of this you state that it accepts paint and finishes. I would agree on the paint but if you plan to stain it at all one must ensure that squeeze out is removed from the surface it it will show. Even with clear finishes like Danish oil and such (I know from experience on that one ?). I found that clamping very tight makes the best bond and only using enough glue to coat the wood. If you have squeeze out dont wipe it off or put saw dust in it, let it continue to dry for about and hour then come back and scrap it off with a putty knife. Easy.
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