Hi Joe
First of all good to hear you walked away from it that's the main thing as for the rest whilst its definitely a hassle it can all be replaced. A lot of the advice and comments you have already had is very relevant but as is always the case in something like this there are so many variables to factor in. I'm 49 now driving since 17 started off in HM Forces with 109,s and a Sankey trailer HGV 1 since 21 and have owned and abused a number of Ifor Williams trailers.
Nose weight and load distribution is critical and often overlooked, I am a pain when loading mine at builders etc watching the guys put on dumpy bags or whatever and always have them over axles but slightly biased to the nose.
Tyre pressures are often overlooked but I know you said not in this case, As has been stated already the high pressure smaller tyres fitted to some ifors seem far more stable to me than the larger ones. Tramlining on some roads can really grab the trailer and initiate sway.
My own experience with a brand new LM 166 tri axle which I towed from Windsor to Northumberland behind a 3.2LWB Shogun ( Worst thing I ever owned ) was initially a nightmare and would start an uncontrollable sway at anything over 45MPH. That was down to the incorrect height of the tow bar on the shogun and once sorted it was ok. The advice to accelerate out of it yeah ive heard that on many occasions but for me to have tried that would have just made things far far worse. My own solution has always been to brake often quite hard, is this the correct solution ?? not sure but going faster certainly wasn't. Best tow vehicle I ever owned was a LWB 3.0 Patrol it just seemed to shake off any wiggles from behind and carry on as though nothing had happened. Currently I use a 3.2 Ranger with a TT126 tipper and have no problems with towing with a pick up, Mind you I am like another member here in so much that I sit at 50-55 steady away when towing. Next purchase is gonna be another Tri axle LM166 as my own experience is they are far more tolerant of the load position etc than twin axles.
I guess you will never know for sure what triggered it but once again as has been said don't beat yourself up over it as you aren't the first and definitely wont be the last
Regards
Dave