That being said - here is my personal take on things. The Lumin A1 is the player to get over the S1 - for now. Why? The A1 is the original (the one I have) and uses the terrifically musical Wolfson WM8741 DAC chips. The new S1, which does handle double-DSD (DSD 5.6mhz) uses the ESS SABRE 9018 Chip. I've personally never been a huge fan of SABRE DAC chips.....but others love them....so YMMV.
Lastly, the A1 WILL be upgradeable to the S1 should Double DSD take off or users decide to go that route for whatever reason.
LOL, the never ending quest for incremental improvements. It was your comment above that got me off the fence and go for the A1 instead of waiting for the S1.
No regrets, really. What the other users here have said about it is true. There is a certain way that the A1 deals with details and nuances that is illuminating

If Lumin is not making the S1 power supply available separately, then perhaps the next step would be the KL PSU, although someone who has heard both says the S1 PSU is better.