I concede that at this point the only true way of separation is to have PvE'ers and PvP'ers in their own universes.
Sounds good to me!
Should they remain in their own universes forever? (using your example, without the conditions I have listed above, PvE'ers will be able to achieve more in the same time frame.. meaning that anyone who decided to have a fully immersive experience (as you put it) will then be at a disadvantage.. at that point the PvE'er could decide that PvP sounds like a fun idea)
If private groups didn't exist I'd agree with you - you start in PvP or PvE and you stay there; if you want to try the other one, you re-roll. However, private groups already give players the ability to bug out of the "hard" galaxy for as long as they like and then saunter back in. I raised this as an issue way back when - that players can use the private groups to, for example, avoid a notorious PC pirate/hit squad frequenting a system they want to get to for something. "Notorious PC pirate you say? Why then I'll switch to an alternate universe (private group), go do my thing, and then switch back". Exploit? Debatable, but definitely a way of doing what you suggest above in an already existing way.
FWIW I argued that a player should only be able to move "downstream" in the relative difficulty settings. I.e. Ironman -> Normal -> Private Group. That had it's own issues in that it didn't cater for people who legitimately wanted to play with a bunch of mates for a while then rejoin the main fray.
Anyway, that's by the by... the "exploit" already exists is the TL;DR!