I just looked at the KZ website and didn't find a "Sportsman" that was 28 ft. long. Most likely, you have an older one. That said I noticed that the weights for those close to 28 ft and above started at 6K and went into the 7000 pound range quickly.
If you are running a 14 inch LRC tire I think you need to upgrade a bit. My trailer runs down the road very close to 6,500 lbs. I had the earlier Marathons that I inherited when I bought used. Got rid of them after the first year, 4th on the trailer because I had some noticeable bumps on the tread surfaces of two of them. Got some Maxxis and were happy with them but I did have to have them balanced a few times. I now am running the Carlisle HD with a load range E rating. These are also rated at 80 mph on the highway which gives me a nice 15mph cushion not to mention a very nice weight cushion.
I have had them 3 years now and have just about 17K miles on them. They still hold air too. Fill them up in the spring and might add a few pounds in the fall. Great tires....so far.