Honestly, I've just been chucking them when I no longer like the hit. If I ran out, I would just switch to the MWA
tank mod setup with a 306 and deal with the leaking (hopefully I found the right O ring now though to stop the leaking). I find when I no longer like it, no matter how much I dry burn and pick at the coil, its only a marginal improvement. In the end, not worth it for me. If its relevant, I'm using a Torpedo Tank.
If you want to do it though, I bought a pair of what they call diamond tipped surgical tweezers from a hospital supply distributor. The tips are like really sharp unbreakable needles and its long. I find it to be the best way to pick crap off coils when I must. Usually use them for my dripping atty maintenance.
Edit: Wait you use a regular sized CE2? Not the XL? If so you are in luck, Healthcabin has them in stock.
https://www.healthcabin.net/index.php?main_page=product_info&cPath=1076_1071&products_id=7760. They have been out of the XL for a while, which has been bumming be out.