Aaaaannnd, for the millionth time I'm not suggesting making everything spec ops or ATR.
It's unavoidable.
You talk about having different mission difficulties, for example. But I assume the harder missions will reward proportionately better, yes? Or everyone would just farm the easy ones. But that means that in order to be competitive, everyone must be able to do the hardest missions, which means only the top players can compete.
Some things are simply flat-out impossible, and this is one of them. You cannot make a square triangle, and you cannot make AI that is difficult enough to challenge strong players but at the same time allow weaker players to make a meaningful contribution.
---
As I see it, there are basically three possibilities.
Option 1: Open Only. You decide to ignore 98% of the playerbase and let the game be run by the 1% of players who are the best of the best. They kill everyone, everyone gets bored like in CQC, and the game mode dies.
Option 2: Solo Available. PVP remains irrelevant, just like it has been, but the remaining 98% of players can have a good time competing to do more pve against each other. If the gameplay loops are interesting enough, the game mode lives, but if the gameplay loops are boring(like in current powerplay), the game mode dies.
Option 3: Solo Available, but with pvp/pve zones. You allow players to play in solo, but you also add pve objectives that can only be accessed in Open. The solo players get what they want, the pvpers get to do meaningful pvp, and everyone wins.
I think you can tell what my preference is.
---
But to reiterate; it is simply not possible to do what you want. You can talk about it all the day long, but you can't make a square triangle. It's not a matter of developer effort or clever coding, it's a physical impossibility.