Thanks for sharing your experience, Crom. Very interesting. I agree with the hysteria created around the USB Regen. Even with my previous system, it barely made a difference. With my current system, it made no difference. A similar hysteria has probably developed with the mR already and so I can't blame you for your skepticism. I suspect for other systems where jitter matters, the mR makes an even bigger difference but even for the Chord DAVE, which is much more immune to the source than anything I have previously owned, the mR still makes a very worthwhile improvement. Any easy recommendation given its asking price.
Your DIY build obviously performs at a high level and so it's nice to see the mR, with a good PSU can at least match it. Your battery is interesting. The 6 milliohm impedance it cites is indeed low but it only cites it at one frequency (1 kHz) so it's hard to know how it performs throughout the audible frequency range and beyond. Paul Hynes' best regulators have measured output impedances of <3 milliohms from DC to 100 kHz and covers the range that John Swensen considers the most important for the mR.
As for the Paul Hynes PR3, which is very similar to his SR3, this is based on the same good fundamental design as his better power supplies but it incorporates off-the-shelf components and are designed for the budget-conscious buyer. This may not be better than the other offerings you see advertised. The SR5 handily improves upon the SR3/PR3 in terms of performance and begins to utilize his custom designed 160VA mains transformer which offer lower mechanical and electrical noise and avoidance of core saturation, what Paul believes can seriously impair current delivery. The SR5 also utilizes even higher power Schottky Barrier rectification, higher power output stage as well as more low ESR energy storage. The SR7/SR9 go even further as these are custom designed to much more precisely match the needs of your particular component. These power supplies, depending on the number of rails, can sell for $3,000-4,000 and are not for the faint of heart but many owners have commented that the difference is there. Obviously, the challenge with Paul is that he has many things on his plate and so turnaround can be painfully long.
Regardless, I will be interested to read more about your battery supply with the mR.