Force Sensitive Archive

We have been through two phase 1 so far. I am interested in doing this 3rd phase 1 Pursuasion Quest. My question is. I have an alt char that did the very first one. Will he be able to do it again. My reasoning is I really don't want to grind the DOC crafting line with my main char again. He is a 4-4-4-0 doc. I quest my question is did anyone do the Phase 1 Pursuasion Quest during the first go around and then do it again the second round.

Chops MBH/4034 Pistoleer/4000 CM