... as I've already stated, this does not hurt a Minion Erebus very much because
even if you kill his whole army, he'll have his whole army back almost instantly by just standing near to the reinforcement waves
Which is why you move him away from them - if he moves back to them, unless a Demigod is tearing them up they don't die fast enough on their own to allow him to instantly have an entire new army - complete with Idol minions. If he tries to kill them to get his NS back, he's not focusing on you - and at this point you should be focusing entirely on him - which should provide more than enough time to get him down and out.
I know what I'm talking about as I've seen that every top player in the ESL 1vs1 ladder (no favs -> no Horn!) started to lose against Minion Erebus when not taking Minion Erebus themselves. This ladder died the moment Minion Erebus became popular because only such players won anymore. Virtually every 1vs1 I try to join in the custom games nowadays has an enemy Erebus.
Ignoring the fact that the game isn't designed for 1v1 Play, I question how much you've seen as General Oak is single handly the best solo Demigod in the game. I've played against an equally matched Oak as Minion LE, and I lost pretty damn badly. His focus on AoE and healing makes him damn near unkillable in the late game.
Minion LE isn't an unkillable, unstoppable force that can spawn his entire Minion army instantly, with no penaltly that is capable of doing equal DPS with or without minions. Killing his minions removes his DPS, and as a Minion LE player I assure you this is the fastest way to make me retreat.