Need new tires

Need to replace the 5 year old tires on my TT and need some advice about upgrading. The trailer is 38 feet and has a GVWR of #9975 and currently has Load Range D tires from the trailer manufacturer. I want to upgrade to Load Range E for a little extra comfort level (no extra weight) but do not know if the rims are suitable for the additional pressure. I pulled a tire and looked on the back of the rim for some sort of psi marking, but nothing that simple to be found. The rim has 5 spokes and these are what what on the spokes:
1) Tire max load #2150
2) Tire max load #2830
3) A960 15x6J
4) 5H-1143 and 6H-1397
5) Made in Taiwan
Around the center ring there were several QA stamps and the letters DOT-T ET0

I have tried researching the numbers on the 4th spoke and found nothing related to rims. I am a little confused as to why the rim would have 2 Tire max load markings.

Any advice on these rims or do I need to bite the bullet and get some new rims to go with the tires?

Thanks in advance
Ken