Don't see anything here saying what the OP decided but I did want to revisit this.
From what I can find your trailer axles are rated at 7,000 lbs each. The E rated tires put you within 100 lbs of your axle rating. If your E rated tires are not up to carrying the weight neither are your axles.
I would be very interested to see the results of scaling the trailer by axle and by side. Basically if you are at 13,900 lbs sitting on the axles, it would have to be perfectly loaded front to back and left to right to not have a tire overloaded.