If you log on to the Princess website, the system can see that you are a previous guest and on certain itineraries you can get a small discount from the current price.
I have seen invoice statement from Princess to a big box TA that shows the commission break down and it could be as much as 11 to 13% of the fare you pay, depending on the itinerary. Lower volume TAs probably get lower commission rate. So you can see there is a bit of leeway for the TA to give something back to you. In the case of this big box TA, you get about half of that commission back in the form of a shop card after your cruise. For a long cruise, this could be a non-trivial amount of money. Getting some chocolate, flower or specialty dinner is nothing compare to that. I rather get a cash card to use later than some OBC that I have to use onboard.
And yes, you can book directly with Princess (onboard or on their website) and transfer the booking to your TA (including big box TA) within 60 days. Be careful if you use Princess Vacation Planner (their internal TA), those bookings are not transferable.
What I don't know much about is the these "group" rates. Does anyone know how much the discount that can be? To get these group rate does the TA have to put up some deposit to grab a block of rooms that they can sell back to their clients? As such your cabin selection may be limited from that TA?