I agree that in first trip / weeklong trip, it is a lot to do both St. Barth's and Anguilla. I understand your motivation - I had the same ambitions when planning our first trip and didn't end up doing either because there was so much to see in SXM. Indeed a catamaran / day sailing trip might scratch your itch for scenery and a little adventure, while still be relaxing.
Where is your AirBnB? With six full days you could do, in whatever order: 1) Orient 2) Pinel 3) catamaran 4)Friar's 5) something on the Dutch side - D's is popular with good food and a nice beach and 6) still have a day to do whatever you feel like you missed, or to the contrary, what you enjoyed that you'd like to repeat. Also, re: Pinel being secluded, I don't know that many people would classify it as such? Yes, you have to take a quick boat ride to get there, but my impression has always been that the two restaurants stay pretty "full" of folks.
If you're dead set on traveling to another island, I would choose Anguilla and consider it one of your more "secluded" days. We spent a day at Straw Hat and while there were other patrons at the restaurant, the beach itself was unlike any I've seen. There just really weren't a lot of people or noise around, and it felt very quiet and lovely.
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