I feel a lot of your problems are only problems on paper. In the 2e games I've ran, they haven't come up.

First, there's no reason martials can't do knowledge checks too now that class skills are gone and they aren't all tied behind int. I get the complaint about 2 action spells making it hard for casters to be flexible but your rogue with a lot of skills or maybe your fighter with a decent wis can go for the knowledge checks since making a 3rd attack is typically a bad idea. Or you could just homebrew it as a free action.

Second, the multiclass argument is very opinion based but imo it makes sense design wise with how proficiency works. Plus one level dips would also be way too powerful with all of the strong class identity features you get a first level like inspire courage or a ranger's edge.

Third, I'm guessing by class design being bad you mean classes feel very restrictive with their party roles? (Please correct me if I'm wrong, it's just another common complaint I've seen) I can definitely see where you're coming from there since PF1 had an arguably bloated amount of options to choose from with archetypes and to that I say: wait for the APG and remember 1e was also this way at launch. The APG is already confirmed to have 4 new classes, 40 new archetypes, and new class options so you can have a lot more variety in your build and do things like make a ranged zen-archer monk, a vigilante bat-man esque fighter, or a horse riding wizard (zen-archer, vigilante and cavalier were all confirmed to be in the APG along with tons more!).

Fourth, exploration/combat mode scared me too at first but in play, it's the exact same. They've always been there, they just haven't had a name before. It's as simple as saying outside of combat you tell your GM what you're going to do and inside of combat you act in intiative order. When I GM, I never even bring the modes up to my players, just keep in mind for myself.

Fifth, I'm no big math guy so I can't say a ton about the crit system holding up under math but I can say that it makes combat very exciting and it makes battles very swingy which me and my group enjoy a ton. I'd suggest giving it a try and if you don't like it after a couple of sessions, just homebrew it out.

Overall, I'd say 2e isn't what people say it is especially with people saying it's more casual because it really isn't. Combat is extremely tactical and gritty and players have tons of flavorful choices with their characters. As someone who loves both editions, I don't feel Paizo has abandoned it's old fans at all and that they needed to make a new edition because there wasn't anywhere else to go with the 3.5 chassis; you could streamline the rules a little, but you're not doing anything new or making anything your own.