Ah, Aiptasia (if it is Aiptasia), how I loathe thee.
I actually have done some amateurish academic research on the topic in the past, although I'm fairly certain both the research paper and the Science Fair Project were done in middle school, so what I remember is probably not completely accurate (in addition to the fact that the actual papers are not here right now).
What I do remember leads me to agree with the suggestions in the link for sticking solely with injection/predation methods of control, as part of why they recover so easily from mechanical removal is that their primary reproductive mode is through pedal laceration, so every bit that is cut off (or left on the rock when the stalk is removed) is programmed to produce an entire new animal. I'm sure that this is not the sole cause, and that the source I read it from was oversimplifying it, but I'm fairly certain that it boils down to "don't cut them into pieces, or you'll just help them reproduce."
My personal recommendation (as it is what I remember as being the most effective aside from getting a copper banded butterflyfish) in this case would be a kalkwasser injection treatment so as to (hopefully) kill off the entire animal and prevent clones from popping up. The way me and my dad got the most impressive results with kalk injections was by drawing up a little bit of Artemia into the syringe in front of the kalk, as that way the polyps didn't tend to retract away from the nozzle (speaking of which, as this is a ceph tank, you may wish to simply remove the needle and just use the nozzle, it works as well anyway) before they'd sucked a load of kalk into their gut. For whatever reason, simply covering Aiptasia in kalk doesn't seem to necessarily work, as they may shortly be found peeking back out of the little pile of kalk they were covered in; however when they ingest some, there seems to be a greater mortality rate.
Edit: I forgot to clarify what I mean when I refer to "kalk" in this context, as I'm misappropriating the term here; when mixing CaO (quicklime) into water to produce Ca(OH)[SUB]2[/SUB], the general recommendation (and indeed, probably the smarter thing to do even in this context--but never let it be said I always did the smarter thing) is to add quicklime into a small vessel of water until no more quicklime will dissolve, at which point you are advised to allow the remaining undissolved quicklime to settle off and decant the fluid into a separate vessel to be used presently ( the "kalkwasser", or the aforementioned Ca(OH)[SUB]2[/SUB]), and the remaining quicklime dried to be re-used in a later batch. What I did, and I do not know if I should call this a recommendation exactly, as I didn't perform sufficient tests to see if the additional disruption of pH and [Ca[SUP]2+[/SUP]] concentration was actually justified by any change in effectiveness of the treatment, was to instead agitate the vessel containing the saturated solution in order to create a suspension of CaO in Ca(OH)[SUB]2[/SUB] solution. The thickness of this suspension varied but was generally between a thick, gritty milk-like fluid to a moderately thick paste. My reasoning was thus: (a) if the suspension had a thickness to it, it was a bit easier to prevent mixing between the Artemia "cap" and the "kalk paste", making polyps less likely to detect something amiss before some was ingested through the oral disc, (b) a "paste" made for a more extended effectiveness period of individual dosages, as local hydroxides reacting with the anemone's tissues would reduce the concentration of [OH[SUP]-[/SUP]] in the vicinity, which would then shift the dissolution equilibrium towards the release of more hydroxide, resulting in more damage towards the organism, and (c), if the polyp failed to ingest any of the suspension, then suspended CaO applied directly to the surface of the polyp might manage to inflict sufficient damage to prevent (or at least retard) further growth of the polyp.
Again, I do not have empirical evidence that "kalk paste" applied in this manner is more effective than a saturated solution of calcium hydroxide, nor did I at any point use solely one method of Aiptasia control, so take the above with a grain of salt. Good luck!