TX
It shouldn't take long at all - it's half your time with that company.
As an aside; I consider loging flying time this way. The Pilot in Command signs the log book. If you didn't sign the log book you are not pilot in command.
PIC U/S I always thought was meant for upgrade training eg. training in the left seat. You are PIC cuz you sign the log book but you are not yet released by the company for the full privileges of a Captain therefore you are under supervision.