Oh, I also found out why an 8.4V NiMH battery isn't recommended for the Grado amp:
Most commercially sold chargers at mass-market stores cannot properly charge those 8.4V batteries, as they output less than the 9.2V minimum voltage that's required to properly charge those 8.4V batteries - and the open-cell voltage of a fully charged 8.4V NiMH battery actually measures slightly higher than that of a fresh 9V alkaline battery (9.4V versus 9.2V). No wonder why most 9V-size chargers are crap; they can properly handle only the archaic 7.2V versions of those batteries.
And what about regular 9V alkalines? Well, an amp that's using them will sound no better overall than an identical amp that's using properly charged 8.4V NiMH batteries - and after just a few hours of use, the amp using regular 9V alkalines will actually sound almost as crappy as the identical amp using 7.2V NiMHs, due to the voltage loss during use with alkalines. Switching to a NiCd with the same voltage rating will improve the sound quality slightly, to roughly the level of an "Ultra" alkaline battery, though the overall stamina of the NiCd will be less; that's because NiCds have lower energy density but much greater current delivery capacity than NiMHs.
The truth is, an audiophile battery-powered amp will require both high voltage and high current. Unfortunately, 9V transistor-radio-sized batteries cannot provide both - at least not in their present form. The RatShack 8.4V/120mAh NiCd batteries come closest to what I'd consider an ideal 9V-size battery for Hi-Fi use (note that I haven't tried the Plainview 9.6V NiMH batteries yet).