I often look in the tree of life. They are the rare reagents in black lotus, and those are often rare. There is always 3 in tree of life, and you can farm there ;)
the transmute recipe is in the housing shop in mooshu or you can go to bazaar but mooshu is cheaper by like a thousand. And the black pearl recipe costs fifteen black lotuses, FOR ONE! :( only wish they were easier to find even when a somehow convince my friends to help me look for some i never find lotuses that might have a chance of the pearl i dont even see the point in crafting quests
The transmute recipes are always available from the vendor who gives the crafting quest. For transmuting black pearls from black lotuses , Toshia in MooShu sells the recipe. Usually these recipes are not located on their main page , so click on the top right of his page to flip through all the recipes he sells to find it.
I think the reward for the Bright Surcoat of the Paragon does not match the effort for finding the regeant. Those Black Pearl are to hard to find and or transmute.