I discovered and many engineers will tell you that a balanced cable is pretty much a waste of money. It might give you up to +6dB of more volume, but that is it.
Without having some measurements for your amp I have no way of telling of another amp would be have better bass, less noise, or even more gain. Hopefully someone with the Audiogd NFB-10SE and another amp can chime in.
A leap that many of us have made is to change headphones or at a minimum get a pair that compliments the sound signature of the HD-650. For me this was the Denon AH-D2000. As you have probably noticed the HD-650 is a tad weak in the bass, veiled at low listening levels, and can lack some of the treble speed other headphones like the HE-500 show off.
If you are receiving the dynamics, bass control and impact, as well as volume levels from the NFB I say that another amp is probably not the best way to go. A half-way decent amp is going to sound pretty similar to other half-way decent amps.
Does the DAC section sound noisy? Does it give you the noise reduction you want when listening via PC?
I vote either investing in more high quality music or another set of headphones.