Find yourself an audiologist and have your hearing check? Won't be surprised if your hearing isn't balanced as most people don't have equal hearing on both ears. It is just that the use of headphone makes it much easier to notice.
Read this: http://www.head-fi.org/t/683406/ifi-audio-nano-idsd-announced/645 (from post #658 forward to the next 5~6 pages). It doesn't address your concern directly, but it should give you a glimpse on how deep iFi has invested into the DSD1793 in order to have hidden features that are not even listed by TI and the confidence they have in this chip's performance.
Remember also that this is a 24bit DAC, so you can afford to lower the digital volume on your PC a little just so you can turn the pot higher (and go over the unbalanced area) without suffering from SQ lost.
I actually haven't ran them long enough to drain them off, so I can't say for sure atm. But one thing that is obvious is that the 1.5V near constant voltage does help a lot on maintaining the same SQ as the batteries are draining away. I'll say you will need at least 4 for the rotation. You will probably need 8 for the whole day. Anyway, here is a battery pack I just finish modding: It powers up the SRM-002 without any problem. There is some hissing during startup but it...