I'm not a truck-nut-ologist, so I don't have much to go on, and it's frustratingly difficult finding accurate dimensions for them online. I have found this ~~delightful~~awful pair (I had to look at them, so so do you).

The entire structure is approximately 40cm tall, and I measure that as 660 pixels, it look like the main 'bulk' of it is in the lower 330 pixels, or 20cm, and about 375 pixels wide, or around 23cm. If we assume that section is half as thick as it is wide, and approximate it as a cuboid (I've rounded the numbers, and unrounded the shape), that gives a volume of 5290cm^3, which is disturbingly close to the value you calculated as necessary. Allowing for the top section, I think they might just do the job.

Obviously those numbers are very approximate, but I've started at that model enough that it'll haunt my dreams, and 'Ten million aircraft carriers' is an approximate enough description, that I think we can say it's within reasonable tolerances of being accurate.