I just do not like short actions in general as they only fit short cartridges and of those I do not like many. I do like 308 and in fact have several but they are new CZ 550 so they are the long action. If I ever decide to convert the 308 to something else I can. If I need to run longer magazine and seat big bullets far out, I can. But as good a reason as that is, this is not typically my reason for the long action. I like 7x57/8x57/30-06 style and length cartridges (I love all classics actually - .375 H&H, 9.3x62/64, .404 Jeff, .458 Lott, etc.) and so I like the actions that go with them. Strictly personal preference. One of my favorites now is an intermediate Type S Mauser in 7x57 and as beautiful, slick and functional it is, I wish it was the regular length action. Oh well, will stick to 57mm case length with that one (or .308 with longer bullets if I were to ever butcher this one - highly unlikely
). Nothing wrong with that.
If you like .308, I say get that ZKK then. I think it is the best one of the bunch. .308 W is a great cartridge, no doubt. But I never hunted with it. I never hunted with a 7x57 either till last year and it impressed me. So now I'm on a 7x57 binge.
I don't think the cartridge choices you have are bad. I'm in Canada and good luck finding 7x57 or 7x64 on regular basis. 7x57 is more common now, so I'm surprised it is not as common in Europe as it used to be. Another plus point for .308 I guess. But .308 is not magical or special. It is just common and more than good enough. There are flatter shooting, more powerful cartridges. The 7x64 for example should have better ballistics than the 308.
On the ZKKs there is nothing wrong with the set trigger an when not set it works better than unset double trigger. For regular hunting though I find set triggers too much to think about and prefer the simple single trigger. On the ZKK the second regular trigger supplied with them curves farther back in the trigger guard for a better fit (to me; and I have bigger hands/long enough fingers) and even more room for gloved finger IMO. Hence the preference.
But I do like old-school German dual set trigger for the coolness factor and for how light you can set them. For target shooting or hunting from a blind/stand or any kind of ambush hunting I think they are great. That's why the rifles you are choosing from, all appeal to me in some way.
Hope my comments make sense.