Update: I figured something out.
I happened to be cleaning my dad's old pc that has G41M-VS motherboard with E5300 overclocked to 3.12 GHz. While I was at it, I decided to test out this psu there. And it started on it. I checked voltages and 3.3v rail as showing 3.61 volts constantly, not dipping, as opposed to 3.58 i usually get on that p4 motherboard that sometimes peeks to 3.6.
So, i got thinking and decided to attach large loads onto different rails. as suggested, I tried attaching loads to 5v rail, but it didn't help. But attaching to 3.3v rail actually makes it more likely for psu to start.
I'm saying "more likely" because it starts on 2 tries of shorting the green wire. (second time shorting (after 1 second cooldown from first shorting) is guaranteed to start the psu.)
Loads I attached were, 12v 80mm fan (to 3.3v rail) and a laptop charger that is designed to go in cigarette jack in cars. (attached to 3.3v rail starts psu. attaching to 5v or 12v doesn't)
(Note, on other forum, they told me that overvoltage protection kicks in at 3.8v actually)
My theory is that when PSU start the first time, the voltage is 3.8 or higher and triggers the OVP, but if a large enough load is attached to 3.3v rail, it brings the voltage down to 3.5-3.6. This specially makes more sense considering the fact that old motherboards were utilizing 3.3v rail to some point while modern motherboards barely use it at all. (afaik)
So we're back where we started but with a better idea of what could be the problem.
Now, here's the important thing I discovered
if I manage to jump start the PSU by adding load to 3.3v rail, and then removing the load and then measuring the load, the multimiter shows "3.67" volts.
if I cut the brown (aka 3.3v sense) wire it shows "3.67" volts.
if I then attach that brown wire to 5v rail, it shows "3.48" volts.
if I attach the brown wire to 12v rail, it drops it down to "3.18" volts.
When the brown wire is attached to the 5v rail, the PSU starts without shutting down normally. No need to add load. it just simply works. Though I'm not sure how comfortable I am with this solution.