With my skills, I would have made a jig, clamped in the piece, and then drilled pilot holes straight through the piece. Then I would have drilled for 2 dowels. After that I would have glued the piece in with the two dowels, and filled the holes with plugs and/or filler.
Still, this would only be marginally better than a properly glued joint, so I would say that you're good. The cedar/whatever shaving might cause a bit of swelling, but it should be marginal and if it's at the top of the crack I can't really see how it would be a problem. A neater fix would have been sawdust mixed with glue, and then using that as a filler.
When you said you action was too high, did you mean the action or the curve of the neck? Hold down the strings between the last and first fret, and check the gap between the string and 7th fret. It should be about 0,3mm - 1 mm, I usually go for a gap the same thickness as a credit card. After that is set, you can move on to setting the action at the end of the neck, keep lowering the saddles at the bridge until it starts to buzz at the higher frets (12th - 24th) , and then raise it up until it stops buzzing/feels comfortable.