If you can at least nail the Hotel California tone, then at least you're in very close proximity to where you want to be, and more to the point, you're not going find what you're looking for in pickup changes alone. Pickup swapping probably won't even get you half of the way there. It's often said that you can play any style of music with any guitar, and conversely, any style of music with any pickup. Pickups matter, but their influence on the overall tone obviously has limitations.
For me, pickups aren't really about tone as much as they are about feel and playing comfort. It's easier to play certain genres with certain pickups, not necessarily because they sound right, but because you don't have to pluck as hard, pick as lightly, or be as particular in your technique to get a certain sound. For examples, Teles and their stock pickups are known for their Twang, but you can make almost any guitar twang if you attack the strings closer to the bridge, it's just that a Tele bridge will give you that sound without having to work as hard for it. It's why they say Hendrix sounded like Hendrix with any guitar he picked up, because he could adjust his style to the guitar, and the end result was always more or less the same.