Before the sync occured, I was waiting on an NPC Shuttle in orbit above Corellia. After the sync took its course, I've found myself instantly back in the starport...but I cannot find a transport back to orbit.

Umm, were you travelling to the starport you were teleported to? In which case there is no issue. If you had just left that starport, then simply get another one as before.

I had left that particular starport on a shuttle into orbit and had waited the 3 hours till arrival there. I'd get another shuttle, but the "NPC Shuttle" option doesn't appear for me within the starport.

Oh. That option is broken. Can you give me the id of the ship you are trying to get to and I'll teleport you there.

The ID is 163647. It's the TMS Greenlight. I greatly appreciate your help.