Received my box-o-bases and love them as always Coco; I'll be sure to post some pics once I get them changed out in my display...it'll be a fun weekend project. The ones I had drilled with a 3/8th inch hole don't quite meet the need so I'll have to try to widen the hole without making a mess of them...they're just a touch off.
I highly recommend the 4.5" round bases for figures with a smaller stance; they provide just enough base and take up a smaller footprint on the shelf. For me, it's all about the figure...so I go with the black round without a nameplate.
I was wondering if the 3/8" hole would work. I bet whatever you were trying to use on them was metric instead of standard. I've ran into that before. Just use a nice sharp, chisel point bit to widen the hole and if you can test it out on a scrap piece of wood or something do that first.
Does what you're trying to fit into the 3/8 hole have threads on the end? If it does you might try turning it into the hole slowly.
Also, I'd like to see a pic of that flying/floating post when you get your figure set up on it for sure.