I don't think that engine anti-icing is likely to have much effect, because that is primarily targetted at ice formation on intakes, not solid ice particles going through the compressor.
Rainboe does make some valid points in that at the moment there is limited knowledge and that a lot of what's there is in research papers, not aircraft manuals - so at the moment sticking to published operating advice is definitely the safest thing to do. That said, those research papers have been prepared by some world-class researchers and subjected to peer review of other world-class researchers before being published, so they are a heck of a lot more than guesswork.
It's clear (for example from the work by Walter Strapp and others quoted by SafetyPee) that there's an issue - hence the FAA/NASA research action that's ongoing. The issue is that *some* rollbacks have happened - albeit 100 in 10+ years is such a rate that most pilots have never knowingly seen it. It's a much smaller issue than conventional icing, if it wasn't we'd all know much more about it. But, I for one am morally entirely behind the researchers trying to understand this better because 100+ rollbacks in a finite period is still a lot, and with enough more there's a risk of an aircraft being lost eventually. That justifies the effort of researching it, and I'd anticipate the subject eventually finding it's way into affected MoMs (starting presumably with those listed by Punka Louvre) and the ATPL syllabus - although I'd guess not for a few years yet whilst the icing boffins try to understand it a lot more (and no doubt publish a fair number more papers!)
G