We towed for the first time over the first week of September, covering about 1100 miles across northern Oregon.
Here's how I tied down the lynch pins:

I left the crossbar in place for our outings with Snowball (the GMC Canyon), and other than a rattle while on rough gravel roads, it did fine:

Another thing that helps stop the rattles and keeps sticky fingers from grabbing things is this hitch clamp:
(Not properly tightened in this image; the bolts usually protrude the tops of the nylocks by a thread or two)

Granted, anyone who is intent on taking the setup can grab an adjustable wrench, but hey, we're talking about keeping honest folks honest...
I have a locking pin for the hitch as well, which stayed in place over the entire trip as the Roadmaster Falcon 2 is a MH mounted drawbar.