What I have feared has come true. I truly did not want the AA batteries to sound best because who wants to change out 8 batteries manually every few hours?
Unfortunately, the native NiMH AA batteries sound significantly better than the Bakoon Li battery supply with internal regulation. That slight bit of warmth and pleasant richness has been burnt away, along with cloying sense of sameness. What is left is ultra clean background with crisp, fresh, resolute clarity and body. Nothing is blurry or murky, and although poor recordings are even easier to identify, their brittle, harsh, thin recording quality is communicated clearly while not exaggerated.
The good news is that Allo Shanti LPS, when upgraded with shorter, better-quality DC cable and fed from a good power cord from a good power regenerator, turns a few sonic corners toward the sonic signature of native batteries. The stock DC cable is found to darken and smooth out the sound a bit at the expense of clarity, but this signature actually improves tolerability of some brittle and thin rock/metal music. Future experimentation with different wires are planned, and I may end up installing a DC jack for easy cable swapping.
No rest for the wicked.. (as I change eight AA batteries and two 18650 batteries for the system).