I've never been to big on researching ways to make EC. I play the game, level toons and i vendor almost all the loot i get from drops. I usually only hold onto XI or XII gear if its modifiers are good.
The reason i need the EC if it helps, is to buy gear mainly two plasmonic leech consoles maybe 3. A couple mil will also go towards XII VR nanite disruptor and polarized disruptors.
I just checked all my characters and i found that one of them has 40 ferengi lockboxes. A different character has 64 Lobi. I think i read something on ESD the other day that you dont open lockboxes with the intention of getting the item you want (i knew this one already). But i think they said that instead you collected Lobi and bought BOE items and sold them and thats where i got lost.
do EC foundry missions daily. it is atleast 500k/char, just make sure your inventory is empty. if you get lucky, you get 700k, if you are really lucky, and you have an eye for it 700k + a good item to sell on the exchange
do gorn minefield (with the side mission if it is available, it is a bonus ) and SB24, get first place, and sell your stuff on the exchange while you can (with the fleet consoles, the reward prices dropped significantly, and with the fleet tac consoles they will drop even more )
if you want you can do the tour, but it is boring
as far as boxes go, I open them for the mining rights, so I just have to park my alts next to DS9, and I am set for a week. you get lobi, which you can turn into a good ship if you decide, and you can get lucky with rewards to sell on the exchange
edit: also you can sell common duty officer boxes from the fleet vendor, if you know how, but they are not selling too well, I kinda pushed their prices to an all time low ^^