If the battery box is not defective, a new one won't do any better. Battery boxes don't amplify.
A CA-9100 pre works great with the H320. Provides 20 dB clean gain for quiet stuff. You don't want to turn the H320's gain above 24 dB at most because then you get into digital gain.
The CA-9100 can also be helpful when recording very loud stuff, because people have reported that if you have to turn the H320 below -0.5 dB to keep the meters from going over 0 dB your recording might well clip anyway. Since the ST-9100 provides attenuation as well as gain, you can attenuate with the ST-9100 if necessary and keep the H320's gain from going below -0.5 dB.