First, thanks to Jeff Kurtz for this idea! I posted my problems with leachate as a discussion in the Stackable Bin Group, and Jeff posted a picture and description that I tried out, with great success.
I drilled a hole in one of the corners of one of the tote lids, then put the lid on three milk crates. I put the bins on top of the lid. I put a small bucket under the corner of the lid that has the hole. The leachate drips into the small bucket. It's perfect! All I have to do is empty the bucket now and again. I originally had the bins balanced on some spare boards inside a larger tote, but that required sponging out the leachate on hands and knees, which was less than fun. This is so much easier! I'm definitely going this route again if/when I set up a second system. Thanks again Jeff!