Going to the larger axles should get you a bigger tire. When you get to 15" tires, the choices broaden. I put Carlisle RH Load D's on my trailer and have plenty of headroom over the weight of the trailer.
I'd suggest, since you have spring issues and are changing the axles, to take your trailer to a good trailer frame shop in your area for this work. The frame shop knows their stuff and will put you back on the road with a setup you can have confidence in. Upgrading the bushings and equalizer would be on my short list, too.