If I was looking for 15's I would probably go with Maxxis - just an opinion. As for load rating, what do you have now? If you have C's, it might be worth going to a D (8 ply rated). Going up a load rating won't increase your carrying capacity, but I like the idea of having a little heavier tire. If you already have LR D's, I'm not sure what might be out there for E's in 15, but if your trailer is only 23' that might be overkill anyway.
And then if you do go up a load rating - then you can open a whole new can of worms in the debate about whether to run the original pressure or go to the max pressure of the new tires...
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2022 Columbus 379MBC (Previous 2013 Rockwood Roo 23 IKSS)
2023 F-350 (Previous 2017 F250, 2005 F-150)