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Location: Texas
You need a low angle block plane.
LN would be my recommendation.
Also, an LN62 would work.
Plane from the front of the drawer towards the rear.
Next time, make the drawer sides proud of the front. It is easier to plane face grain rather than end grain.
...Naval Aviators, that had balz made of brass and the size of bowling balls, getting shot off the deck at night, in heavy seas, hoping that when they leave the deck that the ship is pointed towards the sky and not the water.
AD1 T. O. Cronkhite
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Location: Regina Saskatchewan Canada
You do need a low angle block. I would steer you to the Lee valley offering. But...... ( yes there is one, even if you wished otherwise).
You need some way to sharpen said block plane and that's were things get hairy. Not because sharpening is all that difficult but all the differing advise and options out there.
Blackhat
Bad experiences come from poor decisions. So do good stories.
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You aren't building a jewelry box, hopefully. My preference is to build as you have, with a proud front lap, given the nightmare of fitting fat side boards several times through a few recycled seasons. Fit the guide(s) snug. Nibble down the lap to fit the carcase tightly, and flush the pins to the side board. When you adjust fit there is only a little end grain to fuss over.
You can use just about anything to flush the pins. Chisel, surform tool, rasp, and a shoulder plane; if you really need a plane. Or, a side rabbet, maybe a No. 4.
But ultimately, I would buy a Leigh-Nielson 102 bronze (cute factor only in the bib apron pocket) and drop the pins onto your belt sander at normal juice speed.
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Location: Southern California
In terms of new: either the LV or LN low angle black planes. In terms of used: there are several folks around here who regularly sell older, used block planes. Send a PM to Admiral or Gregory of Sherwood Forest or JClark. Any of these reputable folks will fix you up at a price of <= 1/2 new - more or less.
Your Worksharp will do for honing the blade.
Thanks, Curt
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"Life can only be understood backwards; but it must be lived forwards."
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Sand paper and a wood block is a hand tool also
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Location: South Alabama
A block plane would be good. So would a smoothing plane, such as a vintage Stanley #3 or #4. I would typically use my Stanely 4 1/2 smoothing plane for that job because it's what I have.
You might also consider the Veritas low-angle smoothing plane. I think you'd find it a welcome addition to your tool kit.
FWIW, Lee Valley has free shipping until the 31st, so if you're going to pull the trigger on a Veritas, now is a good time.
Veritas low-angle smoother Veritas low-angle block plane
Steve S.
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