I'm trying to visualize your problem. 2 X 38 X 18 or 2 X 10 X 18 isn't making sense to me???
I used a 66 inch wide NRS yoke cat frame, which is 33 inches between tubes, or 33 inches between the center of one bottom rail to the center of the other. I used a 34 inch wide dry box. I went with a 13 inch tall box, with the hang tabs 3 inches below the top, which left 10 inches below the cross bars. With that height, the box didn't sit on the bottom rails, and because of the diminishing tube size that you mentioned, the boxes didn't touch or rub on the tubes. I have two dry boxes, one is 16X34X13, and the other is 14X34X13. I'd say, grab a tape measure and see what the width is from the center of one bottom/drop rail to the center of the other. I would call that your max width if you want your box to sit on these rails. Then figure the depth from the top of your cross bar to your bottom/drop rail to get your height. It's up to you, whether you want the box to sit on the bottom rail or not. I chose to have one inch more width & raise it up slightly off the rail to avoid any rubbing. I hope this helps with your question?