Atoli already laid out most of your choices, but I'll clarify that there is indeed still a lock on the Midan gear from A8N so it would take 7 weeks and 1000 lore tomes for the i230 Lore weapon. The Palace of the Dead's i235 weapon is probably the easiest and fastest one to get, and it doesn't require a high ilvl to do that dungeon.

From your post, I'm assuming you already have the i200 eso weapon. You can also upgrade that to i210 by running Void Ark and getting a Mhachi farthing, which you can then trade in for an Illuminati Gobdip.