I've always preferred CoV. Each zone has way less wasted space, no being forced to run all the way from founders falls to Perez park for a single mission, and virtually 0 hunt missions or forced teaming missions (speaking of: does anyone actually like hunt missions or click-two-glowies-simultaneously missions? Can't we just ditch those? I honestly doubt they would be missed.) Villains has always felt more streamlined and like you wade through less BS to get to the story arcs. That said, Mayhem Missions are one of the only villainous things where you feel like you have agency to enact your own evil plot. I think CoV would benefit from an expanded set of missions like these where you have some autonomy and are out for yourself. These would be similar to expanded mayhem missions, let's call them NEFARIOUS PLOTS or something like that. They could follow a somewhat simple setup.
Part 1: design your evil plot:
YOU as the villain choose from a list of motivations, e.g. Money, power, destabilizing an rival organization, etc.. while this aspect will change the way the following missions play out somewhat the key here is that YOU get to roleplay what kind of villain you want to be and what your motivation is. Different motivations lead to different rewards (e.g. financial theft gives more drops, ripping off tech could give some sort of temp power, intimidation gives more infamy, just some small scale short lived reward for completing your plot to reflect your choices). Here you can also define your methods. Do you want to be a smash and dasher? A subtle thief who nobody knows was there? A smooth talker who charms your way into power? Choices made at this stage will establish your "style" of villainy
Part 2: choose your victims
YOU as the villain get to choose the location you want to hit, or the group you want to hurt (e.g. longbow, wyvern) ideally from all the paragon city locations and organizations, this way you actually get to go to the "city of heroes" and make some noise. This is one of the best parts of mayhem missions and key to feeling villainous. Again, you are an autonomous villain, you should choose who you want to fight and why.
Part 3: find some flunkies
Every powerful villain needs some stooges. Here you get to pick your favorite group of baddies (hellions, freakshow, etc.) and you basically go on an instanced mission where you beat down their leader to gain their respect, or steal an item to blackmail them into doing your bidding, or kidnap the leader's significant other, some real top dog nastiness to show them who's a villain and who's a stooge. Maybe you want to play a smooth talking charismatic villain? There can be a way to do the mission as mostly dialogue. This could be as combat light or heavy as you choose, again based on roleplay character choices established in steps one and two.
Part 4: time to smash
This is where things go super-mayhem-mission style. You show up in paragon with an army of goons from whichever organization you recruited. Depending on your roleplay choices, these guys could be your foot soldiers in a grand battle, a mere distraction so you can sneak around, or more. But the mission starts with you assigning them objectives (e.g. start taking hostages, kill everyone you see, do some property damage, start looting). These objectives could make the mission play differently (fewer ambushes if the goons are distracting your enemies, random bonus inf from them stealing/looting, etc.). Basically the path you take to your destination will vary somewhat by the way you use your goons.
Part 5: your individual mission
Once you reach wherever your goal is (the bank, the base of operations, whatever) the mission will play out based on your motivations and style (some villains will have a stealth mission, some will be massacring everyone they see). This way they will play more dynamically than mayhem missions but incorporate all the best parts.
Part 6: the escape
Do you really your flunkies or do you leave them behind to take the heat? Do you leave them in a dramatic standoff against the police so the cops won't follow you, or bring them with you as backup to fight the hero(es) who inevitably show up? Again, you get to dictate their actions.
Part 7: the aftermath
Once you're back at your base with riches in hand, do you betray the group you recruited (more inf/bonuses for you but you have to fight a whole pissed off organization) or do you sacrifice some of your spoils and retain their goodwill (could give a temp power that allows you to summon some goons as pets, or maybe a confuse power to make them join you when you meet them on the streets). At this point all the choices you've made in the previous steps will be reflected in the rewards you get. Whichever hero group you agitated will get a taunt effect such that they will be more determined to go after you (not sure how this could work code-wise, maybe just random ambushes now and then would be easier, the point being you made it personal to them).
Obviously this is a very rough idea and many of the steps would have to be smoothed for balance, but I think the core idea is sound. You as a villain get autonomy over what kind of plots you concoct, your methods for achieving your goals, and who you want to make enemies with. Your choices will be reflected in your rewards. The key concepts here are that you get to make choices through dialogue that will affect the gameplay and mission design, the closest in an MMO you can get to having impact on the world.