I'm looking for insight as to which cooler brands/models will sit directly on the rails without the need for cooler mounts or a drop bag to keep it suspended.
Lots of brands will do this just fine. I have a Yeti 110 that would sit on the rails of my frame. However there are other factors at play. For instance if your frame bay isn't deep enough, the cooler will just sit on the floor of the raft and not be supported on the rails. On my boat with 21" tubes it sits on the floor and I have to suspend it, on my boat with 22" tubes it will rest on the rails. If you have an open bay on a Cat boat this wouldn't be an issue.
Off topic... Sorry... But with rocket boxes in slings in your rowers compartment, don't they clang around noisily as your boat rocks?I use an older Pelican Cooler. I had to flip the latches upside down, but it fits great. Plus it was on sale at Costco. Some times i forget to even strap it down. I use it as my rowers seat.