What is the shortest time for PCS orders to get cut?

Once your reclass is approved then you will get an assignment. You cannot reclass while you're on assignment

When I was assigned to Camp Humphreys, ROK, I never received my PCS orders, so at DEROS -10, I went to the G-1 Office. They had my orders on the system, but somehow my orders never got sent to my unit to be given to me. So I asked for the G-1 civilian to print me out a few copies, which was done. I went across the hall and made my HHG pick-up appointment and then scheduled my Patriot Express flight home. I went back to work after lunch and told my supervisor I was leaving in 10 days and had to clear. I was told to GTFOH and start clearing the next day.

Just as an aside, when I got assigned to Korea (verbally, over the phone from my Assignment Manager) I was given 23 days until my report date.

Sometimes you have to be proactive and take your career into your own hands.

As the SFC said, you have to wait for Branch to approve the re-class request. Once it's approved, the HRC Reclassification Section will work with the another section to decide where they need that MOS and you will get your EMPD notification. Just have to be patient.