@grokit:
No way I'm gonna write them off, don't worry! I really enjoy my K1000 even with my T-amp, but I'd really really like more bass. What is it that you didn't like at the HE6 / T-amp combo? I'm feeding the amp with a 12V SLA battery and the K1000 are run in parallel with some 4 ohm ceramic resistors. I remember reading something along the lines that the t-amp sound is tilted towards the higher frequencies as the impedance of the speakers / phones increases, so maybe the K1000 would sound piercing without the parallel resistors?! Never tried them this way, though, and I'm not gonna do it because it would require some desoldering / soldering and I'm too lazy / busy for that. Maybe this was your experience with the HE6 as well?
As I said earlier, I've tried the K1000 with a vintage Dual receiver and got plenty of bass; I've also tried a vintage Marantz receiver and a Sony ES 505 amplifier. The Dual and the Marantz were a bit too unrefined / undetailed for my taste (but quite musical, especially the former), while the Sony was a bit gray and dull, a bit soulless. I'd fear something like the Alesis amp you are mentioning might sound too unrefined as well for me... It's strange, I know, to claim I need more refinement when upgrading from the ultra-cheap t-amp, but for me this little amp is a little marvel and I don't find it lacking too much in this respect. It has a very direct, forthright sound that I missed when trying the at least 50 times more expensive Sony.
A bassy acoustic recording such as George Winston's "Night Divides the Day" (piano improvisations on The Doors tunes) sounds SPECTACULAR through the t-amp / K1000 combo, even surpassing my Stax 3030 combo by a comfortable margin! On most other discs, though, I prefer the Stax.