PS3 controllers: Oily analog sticks

[Andy-Antsinpants]

Hi guys, I've recently bought a used PS3 that came with two original controllers (1x Sixaxis, 1x Dualshock 3).
I discovered the sticks on both to be very oily. After going through the usual cleaning routine with a total disassembly, washing all plastic parts with dish soap (and rubbing alcohol where necessary), and reassembling the controllers, I found out that there's still emerging an oily substance on the stick shafts, right where the seam between rubber and plastic is.

This hasn't ever happened to me with any other controller with rubber stick caps before (Dualshock 2, GameCube, Xbox 360), but I know an old Logitech mouse of mine has developed a similar oily rubber problem over the years. Googling turned out that quite a lot people experienced this with PS3 controllers like I did, but the majority of them just shrug it off as a lack of cleaning, with no idea hinting to the real cause.

So, I would like to know if there's a proper way of curing the problem. Are there replacement rubber caps that won't oil out? For one of the controllers, I plan to buy one replacement stick anyway since the plastic shaft has seen lots of wear.