To make sure I understand what you want to do:
You want a recirculating skimmer to sit under your tank (in the stand) and draw water from the display and return water to the display. Correct?
If so, then the Bak-Pak is out. It's a HOB
So we're talking gravity feed and pump return?
Maybe someone's done it, no one I ever heard of.
If you're going to drain water over the rim anyway why not just put a small tank in there for the skimmer and a return pump. Only difference seems to be the tank. It could even be a 10g wit nothing but the skimmer and return pump. 300 gph
overflow and a tiny pump for a return.
Unless I'm missing something I think you need to rethink it.