I understand why you do what you do, but - again not to argue but to explain my position a bit.
The straps in your scenario are serving two distinct but different purposes.
1) The one you are focused on which is sway control
2) Bonding the towed vehicle to the trailer.
Now up front I totally agree that a swaying vehicle makes for an unsafe tow and is far more likely to cause a crash and for that reason body sway MUST be controlled.
However in regards to #2 above it simply can not be argued that strapping the frame or body to the trailer is preferrable to strapping the unsprung member.
@Mac5005 I've learned enough from you by reading your suspension threads to know I dont need to explain suspension nor physics basics. But for the purpose of explaining my position Im going to anyway.
In either scenario the straps must overcome the kinetic energy of the change of the combined vehicle. I/E when you decelerate from 60-0 that heavy object in motion exerts force onto the straps. That really isnt changed in either method.
What is changed however is that by binding the suspension you are adding a shit ton (very technical value) of potential energy to the equation. Again you know ho to calculte spring rates and rates of force I dont need to spell that out to YOU but for the benefit of others reading this...if you had a 1,000 lb per inch spring compressed 10 inches, in an unload scenario you would generator 10,000 lbs of force against the strap IN ADDITION TO all the kinetic force resulting in the stop/swerve/accelerate action.
This really isnt a question of the rating of your trailer, its a question of the rating of your strap, its hooks, and their attachment points.
If I were in your scenario I would strap the axles or tires to the trailer AND strap the body down the way you do currently. The goal is to form one common "super member" of the load and the trailer.
And all of this doesnt even address the possibility of suspension member failure and loss of taught on the strap/chain. (Which can be just as big of an issue on an axle strap if a tire goes flat)
Snarky comment about nuns and babies aside, it is totally irrelevant how many miles you have towed this way without incident to date. I have a friend that owns a grading business and he tows two upper mid sized skid steers all over the Carolinas (T300 bobcats ~10k each)...has over 100k miles on his trailer and has NEVER strapped either of them down at all. No chain, no straps nothing. By your logic and his experience the safest way would be to not strap anything down.