My live well has an adjustable shut off valve in side for filling and running fresh water. If I don't turn it down to a tickle when I have fish in it, it will over flow into the boat once full because the pump is pumping faster then the overflow can keep up. Not sure if you have one of them in yours? I've even had a few big eyes flipping around in there hit the valve open more.
I believe minnows are a class of fish that remain small throughout their lives. They are part of the food chain and because of their small size we take advantage of their position in the ecosystem and use them for bait. There are exceptions of course but, as an example, for the most part adult golden shiners will typically grow to about 3" - 5" long. Adult fathead minnows will be 2" - 3" long typically.
If the hoses or hose connections are not leaking check :
Live well intake connection, make sure that it is screwed on tight into the transom and that it is sealing.
Could be live well splash over also if you are in rough water, but probably not with your type of leak.
It may still be leaking rivets as they may not leak unless you put a lot of water inside of the boat.
It does sound like you have a bad connection in one of your live well connections!