A few things come to mind, and one of those things relates to your arrangement of bow and stern lines. Few people pay proper attention to this, but if your bow lines slope “forward” from the ends of your boats to the anchor points on the car (that is, the bow of the boat is rearward of the tie-down locations at the front of the car), you SHOULD attach your “stern” lines well forward of the back of the boat, so that they slope in the opposite direction from the bow lines. In other words, whichever way the boat would need to slide to cause the bow lines to loosen, that same motion should cause the rear lines to get tighter. A really good and easy way to accomplish mid-boat attachment of these anchor lines on a kayak is to rig a bridle around the hull with rope that locks up against the coaming when tension is in the line. Now IF this recommended alignment of “stern” lines applies in your case, you can easily attach those lines to your hitch (using this new-to-you orientation of the anchor lines) and whether the cargo box is attached or not makes no difference.
Keeping in mind that any forward OR backward motion of the boat should tighten ONE set of lines (while the other set will do the same if the boat moves the opposite direction), then IF your current orientation of bow and stern lines is the proper method, (this really only happens when long boats are carried on very short cars), it shouldn’t be much of an issue to run those lines either over or under the box to your car’s hitch (choose the route that deviates from a straight line the least). As has been pointed out, these lines need not be super tight in the first place. But there’s another possibility.
In looking at the pitifully vague diagrams on Thule’s instructions, it seems to me that the bottoms of those longitudinal support frames are exposed. If that’s the case, you could attach anchor loops to that bottom surface, ideally with one such loop on each of those two-inch-square tubes. If it were my stuff, I’d just weld a little tie-down anchor onto the bottom of each of those two-inch square tubes, but if you have a drill and wrenches, you could bolt through that bottom surface. Just make sure to drill the needed hole close enough to the rear end of the tube to be able to reach in with a wrench (and if there’s a cap on the end of the tube, take it off). A million options for anchor loops can be thought of, but here’s two. You could drill a pair of holes and install a U-bolt, with the “bolt ends” extending through the bottom of the support frame from the outside. Be sure that each bolt end has a nut both inside and outside the square framing tube and tighten them against each other to clamp the U-bolt in place. Or, just drill one larger hole and install an eye-bolt, again with two nuts applying clamping force to keep the whole thing solid.
Now, the adapting hardware that Thule’s instructions show, at the connection between the two-inch-square tubing of the box’s support frame to what’s shown in their diagram as as the smallest possible square tubing for the smallest possible receiver hitch, looks rather flimsy. Still, it’s rated for a 100-pound load out on those “lever arms” of the support framework, and any load applied by your stern lines will be less, since that will be closer to a longitudinal pull. Also, since your receiver hitch is sized to accommodate two-inch share tubing, there should be a much larger and sturdier connection at that location than what’s shown in Thule’s directions.