Recahrgeable batteries have been in commom use for over 20 years now, I am surprised to see there are still a lot of myths regarding their use. For common NiCd and NiMH batteries, as long as charging current is less than 1/10 of the rate capacity (for example, for a 2000mAH battery, charging current less than 200mA), it can be charged indefinitely without ill effects. In a 12AX7 cathode circuit, the current is only a few mA, so there is no danger of overcharging. However, NiMH rechargeable battery has a very high self-discharge rate (typically >1% per day, especially the high capacity variety), there is certain risk of under-charging the battery over a long period of time if the amp is not used frequently, leading to bias drift.
Normally, for a small signal circuit like the 1st stage of an amp, a little drift of bias is no consequence. However, according to schematics in post #9, the preamp stage in this particular amp is directly coupled to the phase splitter/inversion stage, as such, samll bais voltage change in the 1st stage will be magnified by the gain of the said stage and dramatically change the bias of the phase splitter/inversion stage. For this reason, I would recommend the use of low capacity NiCd for this application, because NiCd has much less self-discharge rate than NiMH, and low capacity battery takes less current (and time) to charge.
For the same reason, if you just simply replace cathode resistor and bypass cap with a battery without adjusting anode resistor to get the same anode voltage, there will be bias change to the phase splitter/inversion stage.
Comparing two schematics in post #9, I can't help to notice that the battery biased circuit doesn't have feedback from output transformer secondary like the original. IMHO, removing feedback has a much more significant impact than battery bias itself.
Without feedback, the frequency response will be very different than and not as flat as with feedback. Typically, without feedback, FR rolls off at both ends. If you have a preamp or receiver with mid-range tone control, it is like turning up the midrange or "presence" knob. How much midrange increase depends on the circuit topology and components used.
The second effect of no feedback is the increase of output impedance. This is equivalent to putting a small resistor in serial of the speaker. This serial resistor devides the output voltage and reduces the power to the speaker. Obviously, how much impact it makes depends on the impedance of the speaker. If speaker impedance is independent of frequency, then this extra output impedance has no impact at all on tone balance. However, all speakers have frequency denpendent impedance curve, typically higher at high frequency and lower at low frequency (some speakers have dramatically different curves, but that is a different story), excluding the resonant peaks and crossover regions. The higher the speaker impedance, the less of this voltage divider effect. As a result, this extra output impedance has less attenuation on treble than on bass. This is equivalent to slightly turning up treble control and turning down bass control at the same time, leading to an overall brighter tone balance.
IMHO, the combined effect of frequency response and output impedance change because of removing feedback is the cause of the difference DanTana experienced.
One more point is that rechargeable battery in cathode circuit does pass AC current freely. However, since these batteries have very low internal impedance (typically less than 1 ohm when fully charged), a few mAs of AC current only generate a few mVs of voltage, about 1/1000 of the AC voltage when a 820 ohm resistor is used. As such, there is no need for bypass cap and there is no negative feedback in cathode circuit, leading to much higher gain.