OK Tireman9 here, an official card carrying member of the "Weight Police"
Seriously, some comments.
RE the Original Poster's numbers. I would really be interested in learning the individual numbers from anyone who has done "4-corner" be it Escapees, RVSEF, on a closed State scale, State police portable or homemade scale.
The primary reason for 4-corner is not to get concerned about a 250# (5%) difference in individual tire position weight but to identify the outliers with 1,000# difference side to side which I am told is not that unusual.
I have posted several times both in my RV Tire blog and on various RV Forums that until you get confirmation with side to side weights that I suggest you assume a 53/47% side to side weight split. I have received scale numbers from a few folks and they were +/- 1% from the 53% figure for the heavy end of the axle. I have had 4-corner done 3 times (RVSEF and State Scale) and my Class-C runs at about 51.5% to 53.1% heavy for the heavy end of my 2 axles. I have also done a couple CAT scale readings just to ensure no significant "weight creep".
RE doing 4-corner on CAT. This is against CAT corporate policy as they say loading the platform way off-center can affect the scale accuracy and calibration. If you look around you will see that many CAT scales now have guard rail near the platforms to prevent off-center weights.
While I haven't looked at the Escapee scales, I have compared the RVSEF scales with some State Police scales and they appeared to be the same units.
The whole objective of getting tire weights is to avoid overloading your tires. No, your tires aren't likely to "blowout" if you have an extra 1% on one side vs the other, but if you discover you are at or above the load limit of your tires by 10% then you are really "consuming" the tire life faster than you might expect. This can result in a belt separation if you also push the speed rating for your tires in RV service (75 mph max).
Most folks never have belt separations on their cars but we all know that many RV owners have tire problems. One of the main reasons for this difference is that most cars are running around with 25% to 35% reserve load and are driving 20 to 40 mph below the tire speed rating for regular auto usage.
RVs, on the other hand, are running with 5% or - 10% reserve load and from 15 below to 15 mph above the speed rating for their tires when in RV service.
To address the calibration issues both with scales and pressure gauges. My Gauge tests find between 8% and 15% are off by more than 5 psi with a few reading about 10 psi high which means that those owners were running their tires significantly underinflated.
All of this is why I suggest adding 10% to the minimum inflation required to support the load when you consult the tables after you use the heavy end of a 4 corner weight or the 53% figure from a CAT scale.