Ah yes, the joys of flatbedding. Speaking of "true weight" reminds me of the many times loading lumber or steel. Ask a loader what a sheet of steel 30 ft long, 1/2 inch thick and 10 ft wide weighs and listen to the stumbling answers. Sadly, the usual answer is "don't worry, we always load them this way". Sure thing buddy, the fact that you dress like you're sleeping out here among em, haven't bathed or shaved in a month and have 3 times hit the headboard on my trailer gives me lots of confidence in your "judgement". On my own rig I ran an air guage connected to the air bags on the tandems. A certain PSI told me when I'd hit the correct weight there. Otherwise, it's a guessing game. DOT doesn't care what your shipping papers say; if they say 50,000 pounds and the actual weight is 60,000+ too bad for you. You're supposed to know. That's why a good FBer carries listings for every CAT certified scale in the country. Better to find out there than make Mr DOT's day.
What would your options be after discovering you are overweight at the CAT scale? Apply for overweight permits via phone? Re-arrange the load with "come-alongs" and crowbars (if distribution would help)? Go back to the shipper and try to get some of the load removed?
I can answer that... Its easier to carry the weight than it is to pull it. If you want to experience it for yourself get a 50 lb. sack of dog food and put it in a wheel barrow and pull it up a hill and over a few bumps on the way. Then try the same hill and bumps with you carrying it...its much easier to carry it.
California split axle limit is 39,000. I haul 47 -48,000 lbs loads all the time and have never had a problem with axle weight, the split axles usually take a few thousand lbs. off the drivers. Eventually, You will learn were the sweet spot is on the trailer and not worry about being overweight on the drivers.