Really because the current PvE content is so easy you don't need that much gear for any of the Ops.
HM EC requires Full itemized Rakata - stock Rakata is terrible.
Nothing in the game right now requires Black Hole/Campaign gear.
You can do Story EV/KP in Recruit and HM EV/KP in Battlemaster.
You could try Nightmare EV/KP in Battlemaster but I suspect that you would have one heck of a tough time.
You can do HM LI in a Recruit Battlemaster mix so FPs are EZ.
HM EC would require itemized War Hero with 14/14 Augments. It would be doable, but tough (you might need datacron bonus).
I guess you could do it as a self-imposed challenge, but that's what 8 manning 16 man Ops is for