You have the key to your own dilemma. You state you are picky. If I may ask, are you open to your potential long term partner having kids, or not?
Women, on average, want to be in a committed relationship, and more often than not, are happier with sex within the confines of long term relationship/marriage as affection is more important for women (on average). The feminist agenda is definitely moving away from the tradition of getting married and having kids, but it does not talk to what most women want. Surprisingly, women who are married for a long time and have children are happier than sexually liberated / independent women (but, that's a discussion for another day). Outright stating that marriage is off the table may drive some away, especially if such a woman does not have children. You may be sabotaging your efforts here.
If you have a reputation of sleeping around, women will most likely avoid you if they are looking for something long term, but those that do gravitate towards adultery and multiple sexual partners will approach you more often. I would definitely look to spend time with those that are more discreet (which I admit is probably a lot harder than it sounds).