my main question is ... Why having chosen such " monster size " mosfets ???

1) Imagine some kind of Halogen lights as a load: the inrush current can easily overload the switching supply ...

2) have a look to the pic voltage regulator : no big caps around it ... so, no supply weakness could be dampened. ( switching supplies ALWAYS have load response time - enough to lead to a pic reset )

as everyting fine without heavy load , it's correlated to load inrush current ...

just need a test, powering the Pic with a small "Duracell" battery - say 4v5 - and the load with that big power supply ...