This is how guys built cyclo cross bikes before they became main stream. If you couldn't afford a fancy purpose built European bike you simply used an road bike, and if you were lucky you could afford to have someone weld canti bosses on it.
As an actual racing 'cross bike the end result will be heavish and the lower Bb may cause problems. This will likely make a great gravel grinder for running fast on dirt roads.
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk