Happy Birthday. Cruising French Polynesia is a great way to sample the different islands. You are traveling so far; please do try to stay for a few days before you return home. I recommend a post-cruise stay over a pre-cruise stay. You can ferry to Mooreaa from Papeete in less than one hour. You can disembark from your ship and roll your suitcase across the parking lot to the ferry dock.
If you find a good fare on the Paul Gaugin, do try it. Don't be fooled thinking that the 10-day on the Tahitian is a better bargain. If it is the itinerary that includes the Cook Islands, the ship spends a full day at sea traveling there and one coming back - and the water is usually quite rough. Much of the time, the ship is unable to dock in Rarotonga (the Cook Island that is on the itinerary). I typically enjoy sea days -- but I did not like sea days on the Tahitian Princess. I did not like the ship and did not want to spend any more time on her than necessary.
That being said, please know that this cruise was one of my favorites because it was so delightfully social and the passengers, mostly couples in our age range, were lots of fun. All of the port stops are wonderful. The entire place is beautiful.
I am a diehard Princess fan but this is one time that I would not recommend it. If this is the only way you can manage it, then by all means, book the Tahitian and don't miss out on French Polynesia.