I think that the problem is that people try to PvP as an ends. PvP should really just be a means to an ends. If your goal is PvP, as counter-intuitive as it sounds, you should make your goal something other then pvp, but that pursuing would produce PvP as a natural side effect of trying to achieve that goal.
This.
There are various ways to do it. They attract different sorts of people, and have their own typical types of internal conflict.
EM's approach to this is well known (I think?) and seems pretty tested: loyalty to (the underlying needs of) a faction (as we interpret them) which has live targets AND active vigilante policing of piracy within a particular area. When one area is quiet you focus on the other. Your internal hawks and doves sometimes slog it out, as do your want-my-fights-NOW types and your taking-the-long-view types. There's the occasional framing issue when a member or ally gets upset at you prioritising political crimes (which are mostly made-up crimes about slavery) over capsuleer crimes (which are where players are jerks to other real people).
When I (player) was with Rote Kapelle and throwing ideas at how we could frame what was, essentially, a desire for "All PvP; all the time" we touched base with Rote's rich (and sadly neglected) background as a hardline transhumanist breakaway group with strands of ethical egoism and anarchist illegalism. It's about cultivating strength, excellence and joy through competition, and applying selective pressure to other capsuleers who might therefore grow into their transhumanist nature. That's the nearest I've seen to an RP framework to wrap around PvP-for-its-own-sake. While it has the
potential for RP, in reality it's been more of an RP-very-lite nostalgia thing, with newer pilots not having an interest in RP.
Let me reinforce that when I'm talking about striking a sportsmanlike attitude with another RP group for PVP, I'm not talking about setting up a tidy schedule of pre-planned fights a la the tournament or doing anything that would artificially break IC logic. I am talking about both sides respecting one another as players and acting in a way that encourages fun-having in order to enrich and continue IC interaction and PVP without either party growing to resent the other OOC.
I don't think it needs to be said, but do also PvP against the many non-RP groups around you. You'll end up with some "usual suspects", and may even develop RP or semi-RP hunter relationships with them which can be a lot of fun. But... have a hard think about why you fight, what you want from it, and what it means IC for you. There are ways to make the pursuit of ~goodfights~ make sense, but they require thought above and beyond normal framing. We have some relationships where we're essentially trying to stop some people from pirating too much in our neighbourhood, but we're pretty sure they'd help defend it if the second Day of Darkness came. Those are quite different from the people who simply need to be made to see the error of their ways and be somewhere else, or doing something else, whatever tools in the EVE diplomacy toolkit that takes.
And Merd, I was thinking in terms of sub-cap split-and-bait, but yeah, our version of that was that PL's tendency to hotdrop when bored in Amamake did kinda suck. It was a real in-game thing, though, and a reminder that even in the Republic we weren't immune to what was going on in null throughout the cluster. For us the main strategy was to warn people, work around the hazard, and wait it out.
(Also, to be frank, if we manage to evacuate Sahtogas Mata wouldn't particularly object to using FW simply as live-fire training from then on. We don't "believe" idealistically the way some people seem to think we should, but we have our reasons in the Long Game for what we do.)