In theory, using balanced XLR should eliminate noise picked up my the transport cable. It's the whole point of balanced audio, after all.
But hiss can have many sources. The hiss can even be from the amplifier itself. When this is the case, then the best way of lowering the hiss is to lower the amplifier gain/volume and increase the source's output volume. I believe this will give you the best audio quality, but I might be wrong. My experience with car audio has told me that lower gain on the amplifier just sound cleaner. The only way I can see the opposite being better is if you have a very bad source.
I'm 99% sure the hiss is from the amplifier itself, as you describe. So it sounds like there is no issue with lowering the gain on the amp and raising the source volume? I plan to do just that in the future.