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I'm guessing you're not going to be using a mahogany floor for work, so strength isn't a real problem. I think I'd rip down a piece of clear pine, stain it to match the finished mahogany, (use a piece of your cut off mahogany and put a few coats of finish on it to see what the final color will be,) then stain the pine for as close a match as you can get. Glue in the pine strip with epoxy, or Titebond II, then finish it all together. Another (easier option if they're nearby) would be a piece of mahogany decking from Home Depot or Lowe's, and rip down a strip to glue in. If it's going to be on the bottom, a perfect match won't be critical.