I would not lash it upside down. The sheath doesnīt hold it firm enough too prevent loss if the button opens accidendly. I would only lash the sheath to the strap if there is an extra strap for adjusting or holding equipment. You could use a generous amount of paracord or duct tape to fasten the sheath. Make sure to run some of the tape or cord through the belt loop.
I would not run the lashing over the padding of the strap. This could get very uncomfortable.
If you can make a special sheath for the backpack this would be the best solution.
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If it isnīt broken, it doesnīt have enough features yet.