A combination of doing daily crafting writs on multiple characters and doing veteran pledges does it for me. Doing a regular daily random normal dungeon through the group finder system also gives an option to receive purple jewellery. I personally don't think dolmens are such a good options since they tend to drop green and blue jewellery much more often.
I know this is old, but I want to put in my two cents for future searchers.
Finding purple rings and deconstructing is not worth it as of 12/25/2021. Not every purple ring/necklace will net a zircon. You need 10 of them. On average I estimate you need 25-30 purple rings per zircon plating. That is absolutely BS. I still see people recommending treasure hunter. Funny. That is totally worthless. I promise I still find just as many greens and blues as everyone else on my character that has treasure hunter. Its a waste of 50 CP, well, it would be if the crafting tree was worth a damn.
The fastest way is to earn gold by upgrading wanted items gold and sell them. You can turn a huge profit on the most wanted items in the game. Either find them on your own, or find someone selling the item with the correct enchantment. I find this to be the quickest way. I've never found a Briarheart infused bow in the wild, and I have tried and tried and tried. Jewelry upgrading is absolutely broken compared to armor or weapons. No doubt about it.