a 350?? WOW, that must be massive. I run with a yeti 160 and think it takes up too much space in the cockpit.
OP - surprised you find the transom box kind of small. I can easily fit 4 60# tuna in there and still have room for other species. Any more bigger fish, the heads are coming off to create more room. I use the yeti more for extra ice than as a fish box.
I leave dock with the follow full of ice. Transom mounted yeti 50 with ballyhoo, transom 270 full, yeti 350 full, two igloo 70s in mid berth and sometimes an SSI 200 on bow. Let's says a few fish have come aboard for a long ice nap