Thanks everybody for your input.
So after more attempts : filing a little the slot without going deeper, lubing again all contact points (bridge included) and using locking tuners the problem remains. So the culpit was a silly tremolo block design !!! see the pics below.
The first one is the Concord III : brass tremolo block seen from below. The holes are not deep enough so a long part of the string goes through it (On a Tele or PRS this is OK as there is only one contact point on the bridge.) But in this design the string is fold in two places : saddles and upper hole of the tremolo block block. This is probably the root of the problem.
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Here is the tremolo block of my guitar n°1 (early Jeff Beck Strat) the holes are deep :
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