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That clamping jig is genius!
If your saw bends while sawing, it is because you are cutting on the push stroke: Japanese saws like this cut on the pull stroke. It is next to impossible to cut straight by pushing like you would with a Western style saw - they are just too thin. Try pulling the blade across your line and things should improve. Nice instructable, though - makes me want to apply your magnet idea to a sharpening jig.