@OP- Yikes. I just upgraded to Kumho Radial 857's and couldn't be happier. You'd also have to make sure your rims are rated for 65psi, but the trailer pulls SO much better now that the poor tires aren't at 95% capacity all the time. For additional value, they have a speed rating of 99mph (not that I would ever do that, but the headroom is comforting) and significantly more weight carrying capacity than most of us need.
Get yourself a proper alignment, or even look at upgradin the axles. We went from Al-Ko 3500lb units to Dexter 6,000lb with upgraded springs and proper brass greaseable bushings. Going to 15's won't solve anything.