The Kojaks are not that robust; my own front tyre is showing more cuts and damage than I am used to seeing on the front. This sentiment is echoed by some on the Moulton group. However, I am likely to get another set for my Birdy for commuting.
I can't really say about wet riding; I am so careful in the wet that I don't stress the tyre grip so probably don't go close to the tyre slip-out point. I have heard previously that the Scorchers are slippery in the wet from only one other person in the past. I wonder if this is due to newness? IE ride the new skin off it first before judging. The new skin might contain release agent for example.
For tyre bead seating, try talcing the tyre beads well before inflating, and give them a roll/twist after the first few strokes to try and get the beads into the rim hooks. You could also inflate past the maximum (and then let them down again immediately) to seat the beads. I don't know how close one would get to wrecking the carcass doing this - presumably the carcass threads are designed to take tension well above the tyre maximum without breaking.
I don't think there is anything wrong with the Primo Comets. Perhaps more robust than the Kojaks, they roll quite well enough.
I am currently trying out Schwalbe Duranos on one of my bikes; these are good too.