Without drilling holes might be tough. The only two things that come to mind would be to figure a way to make the hardware in a fashion that slides or clamps on to each end or to the handles for one, or to manufacture a "ring" that would fit the Go anywhere in the same way the Kettle ring works. Both options would seem to me to be a lot more work than drilling a few holes.
I used to have a small grill similar to the go anywhere, I drilled the wholes and attached the hardware with bolts and wingnuts, made it real easy assembly and removal, worked great for campouts and such. In my case, the way I had it you could not close the lid when using the roto, but i managed to cook some pretty good stuff anyway.
Let us all know what mod you come up with, might be useful to some others.
Weber Performer with rotisserie ring, 22.5OTS, Maverick 732, Weber Smokey Joe,PBC Smokenator/Hoovergrill, variety of microbrews, Gin and tonic, variety of lighters.