So I recently came back about a week ago and have been playing around just doing PvE stuff and I agree, in order to attract a decent population the game is missing something on the PvE side.
I'm not going to say I have the answers because I don't, but some of the things that I think could help are below. I think those that have done a serious amount of PvP will agree, PvE is an important part of every PvPers life in this game because you lose all your stuff when you die and most cannot afford to just keep running around in new bots after a bunch of PvP(assuming you don't just use t1 equipment). You have to PvE and rebuild your stash so it is very important that aspect of the game becomes better even for PvPers.
1) Life without a corp should be possible on beta/gamma. I have this weird dream that I would greatly enjoy it if this game had some sort of "player housing" where you could just find some open space on a island and start building a habitat(small one) that could not be destroyed and you could base out of. Maybe this idea is flawed but I think the important thing is making it enticing for players to move to beta/gamma and have SOME safety and a place to base out of beyond the public terminals, encourage them to spread out, or form small loose-knit communities. People like to build stuff - but not all people like communistic corps where only the leader(s) get to build stuff - give us more solo or small group buildable content that cannot be destroyed by pvp - but base it in pvp zones. I think this could easily be implemented by some small tweaks to resource costs(don't make small house cost 50 trillion titan ok) and protection attributes of the gamma stuff. Keep the bigger or more important stuff destructable - compromise is key here if you want the most people participating as possible.
2) Central trading hub/island that links to all the alphas and maybe even betas. Travel time in this game is a killer and biggest boredom to me. It takes long enough to travel for assignment objectives let alone trying to go from one alpha to another. I like big islands but I don't like huge trips between them.
Just some ideas, but a +1 for the OP and more PvE stuff that integrates closely with PvP stuff and thus can appease both crowds.