You are correct. You can expand your search to include Brinkmann Cimarron, Brinkmann Southfork, Horizon, and Yoder. You should be able find a good used one on CL at a reasonable price. All have affiliation with Oklahoma Joe and are made 1/4" thick. I bought my brother a Brinkmann Cimarron for his birthday and he is very happy with it.
OK Joe's Longhorn & Vertical Roasting Oven, Brinkmann Cimmaron,'69,'73,'84,'89 Weber Kettle