If I were you, I'd ignore about 90% of the posts in this thread. It doesn't matter how much air is in your tires. If the bead didn't pop when you rolled it into the trailer, it's not going to happen inside the trailer. And even if it did, it only takes a few minutes to reseat the bead.
Secondly, there's absolutely no reason not to strap to the axles. From a loading/dynamics perspective, it's pretty much the same thing as strapping to the tires. You need to make sure that you have four separate straps or chains connected to the vehicle. I prefer to have them vaguely radiating from center of mass out. And make sure that you have the proper type of strap or chain for your application, and that it's not rubbing anyplace that might damage the straps or the vehicle (this is often the problem with X'ing the straps, btw) A lot of people strap to the tires because (especially with cars) it's the strongest and easiest place to run a strap. But this stuff about how you're going to break the track bar? If you break the track bar bolt or a leaf spring bolt while strapping your vehicle to the trailer, then your vehicle is a hazard to the public and shouldn't be allowed out on the roads to begin with.
Also, strapping to the chassis is inherently difficult. Something like a Jeep is particularly bad, since you'll never be able to get the straps tight enough to compress the springs down to the bump stops. Instead, the vehicle will sway and bounce, shock loading the straps, the D-rings, etc, causing premature wear, degradation, and failure. Commercial haulers use mechanical or hydraulic winches to draw the cars down. That's not an option that you have available to you, and even if you did, your Jeep is sitting on a piece of 3/4" plywood and some undersized Z section crossmembers. Frankly, I'd be a little concerned about the damage that you'd be doing to the trailer.
Finally, your junk is inside an enclosed trailer. How's the popo going to know if it's strapped down at all? Besides, it's *inside the trailer*, so it's secured by default so long as the door is closed. That said, I'd definitely strap it down as described above. If nothing else, if you get into an accident, the trailer might get junked, but your rig will be safe inside. I know a few guys that have wrecked their enclosed trailers with their rigs inside, and the rigs came out of the deal unscathed.