ive never done this. but ive seen other set ups in person that work. i suggest buying them at like a sams club though to save money on bulk buying. it takes a ton of straws.
if you buy the kind with the brown papper around a bundle of them you can just use a band saw to cut them.
If it will help, it makes no difference if the water moves through the media or if the media moves through the water. If you are past the design stage, I guess this won't help.