So, let me see if I have this right. You want to be able to play your way, whilst denying the right for other people to play their way when, in fact, everyone has the choice to play whichever way they want. You can play your way and/or their way. They can play their way and/or your way. Seems like what you want is to restrict everyone except you.
Secondary observation, while I'm here. You also say that you and your fellow PvPers want to compete against each other. If this is true (and we all know it isn't

) Then this is easily solved by creating the PvP version of the Mobius group. Funny though how you guys never want to do this.
No at all. I've always said have multiple community goals and lock them to modes, one for group/solo and one for open. That way you can have blockade goals take place in open without all the traders doing their half of the goal in solo mode. Some players will always choose the path of least resistance but a lot of players will want to do the goals in open. Play it your way? Everyone gets to play how they like without interference from the other modes.
As for the pvp group thing open players want a living breathing galaxy where you can get jumped by a pirate and the pirate can get jumped by a bounty hunter. The main things holding that back is the lack of a proper criminality and consequence system which is the cause of the majority of problems regarding "griefing".
I'm coming at this from two perspectives as well. I've been trading in open since release and half the time I was crying out for some piracy. Any npc I could splat in a trade ship or run away from without taking damage.
Now I've turned to player piracy (due to being put off of trading by the amount of people abusing the beacon exploit) and I find most of the problems related with it are due to poor communication game mechanics. A lot of traders turn off local chat and think they've been killed for no reason when in fact the pirate has been talking to them all along.
Some of the time they get their drives shot out and lose a bit of cargo, some of the time I'm letting people go due to the low paying cargo they're carrying. A lot of the time I end up making friends with the players I've pirated as they understand the food chain. Yes the odd trader gets killed because they try to escape, fight or would rather abuse you verbally. Some times the trader will fight back and drive you off. The majority of the time however they combat log. Why play open if you aren't going to deal with the consequences? Same goes for pirates who log against bounty hunters as well.
The other day I was hunted by bounty hunters and due to mistakes of my own I was killed 3 times and lost 6 mil. I was run out of a system and it was impossible for me to get back to piracy without getting killed and was forced to fly 100ly away and try to find a new place to pirate.
That's the food chain cycle which players want in open. Starting a pvp group isn't wanted because open players don't want a "fair fight" as in "10 minutes, first to shields down wins". They want to prey on the weak and be preyed on by the strong themselves (from a pirates perspective). You want to pull over a T6 and then be fighting for your life the next minute because it was a trap and 3 of the T6's wing m8s in fdls drop in to the instance. Emergent gameplay.
If you think this is unfair then you have the choice not to play against other players. Piracy isn't ever going to be "fair" anaconda vs anaconda it's going to be a pirate preying on a weaker ship and being preyed on themselves by a bounty hunter in a better ship or a well armed and efficient npc police force (which doesn't exist right now).
Players want to play with the danger of knowing their next jump might end in death due to getting shot up. The problems that occur are the lack of consequences for the player doing the shooting. A lot of this is around already but it's player created due to the lack of criminality.
The majority of players playing pirate like this aren't clearing their bounties. The problems come from the players who are just jumping in killing a player and then off to the station to pay their way clean. This is closer to griefing due to lack of game mechanics. Piracy done right isn't griefing.
A lot of the players who cry griefer because they got shot in open are blaming the players for this behaviour rather than FD for not having proper consequences and deterrents in place. As a pirate I want to be chased across the galaxy looking for a safe anarchy station to dock at rather than boosting in to the main station in a system I've been pirating for the past hour without consequence.
Players get killed by pirates because we think you're stalling for time to combat log. There's nothing in place to dissuade it so the only way to pirate effectively is to teach players that lack of cooperation will be met with death. This isn't the pirates fault, if you've been playing for an hour and 5 people have combat logged on you without consequence then you're going to react more harshly to your next "customer" instead of taking the time to have a meaningful player interaction featuring roleplay and chat.
The other thing is open should be labelled more fittingly to describe the above gameplay. If people don't understand how the game is played in open then they should be steered towards a different gamemode. They should implement a proper pve version of open (mobius style) so people can play with the rare and meaningful pvp a large number of people desire (although proper criminality mechanics would make pvp more rare and meaningful in open).
Now I get that a lot of players don't want this, that's fine and that's why you have the choice to opt out of it to solo or group and shoot your 1 millionth procedural generated npc next to the same procedural generated asteroid.
All that aside I don't care about people playing in solo and group. Play it your way. When it comes to things like community goals where you have players actively working against each other, the ability to do it from a different mode creates tension in the community on both sides.
In open I have choices about how to play against other open players. I can run, fight or cooperate. When I'm in open playing against a solo/group player I can't interact with I have no choice to do any of those things.
All we want is the option to have
somethings locked to a mode not everything.
I have rl friends who I play with in group so I want the the ability to switch on occasion but I don't want to be forced by the game mechanics to be forced in to a game mode I don't want to play because I feel that's the only way to compete. The same way I believe that solo/group players shouldn't be forced in to open to compete.