I agree, it's overkill with an Edge trem.You don't have to slack the strings with an Edge, the knife edges are quality enough that they can handle the height being adjusted under tension. The advise to slack the strings on a lower quality bridge is sound, but a bit overkill with a good quality bridge
Bit the bullet and removed bridge and studs to check. They are indeed locking screws and the 1.5mm key works. I think it's because the tiny size key gives less tactile feedback and as you say it takes so many turns to tighten.I can't explain why some people have so much trouble seating an allen wrench into the set screw. Possibly because after you do you'd have to spin it so many times to hit lock you don't think it's seated anyway. Try unwinding it, it's much closer to fully unlocked and will stop at fully unlocked letting you know, the wrench is seated.