...I plugged to the SATA line the only thing I had at hand, i.e. a small SSD drive, that pulls exactly 5V 1A.
And it worked!! AWESOME, the 3rd Apollo has been mining and stable for one odd hour (vs. shutting off power after a few seconds or just one minute) and I think that this smart little trick solves the issue very nicely.
The bottom line - beware of cheap non-modular PSUs but if you use one keep it "alive" by plugging something to the 5V rail.
Now I am thinking

what can I add to this set (I need to keep my SSD) for my friend so to make the whole thing work. Maybe a fancy USB gadget like a mini-vacuum cleaner or a few USB fans would do, plus a SATA to USB adapter cable of course - any ideas?
Ah, @philipma1957, thanks for the links to better PSUs, the modular ones around 500-650w are my personal bet for powering up bundles of 2-3 Apollos if I buy a few more of them.
Again , thanks to everybody for your very helpful insight.
Haha wow learn something new every day. I guess they must use the 5v rail to power the 12v mosfets....thats a dirty and cheap trick but would explain why the 12v rail fails on higher loads.
If you have to power the 5v rail with something anyway would be cool to retrofit a 5v USB hub and hook up some moonlanders to it