It's just that there's something profoundly bizarre about using the name of a religion with an "ist" on the end to signify the violent part of that group.

It's simply meant to signify an ideological fanaticism, like any other ideology with the suffix "ist". In Russian revolutionary politics for instance, there were Bolshevists, Social Revolutionists, Ultraleftists, Rightists, Centrists, and a heap of others. In this case the ideology is based on a religion. - Maybe distorted (or maybe not), but still obviously based on the religion. Hence, the word "Islamist" instead of "Moslem" - but you say that you do get the distinction, so I won't harp on that.

Should we call militant Jews "Jewists"?
One possible term would be "Judaicists", for instance in referring to expansionist militant Zionists.

How about Christians that bomb abortion clinics - "Christists"?
Um, I think they're called "Fundamentalists".

I don't remember voting on the word "Islamist" to take on the meaning you ascribe to it. It just suddenly appeared one day as this new label. Had we used the term 20 years ago, I would think it would be assumed you were talking about someone of the Islam faith not some subset of it.
Well, it's common and understood usage now, so I'm just using it according to the definition everyone has agreed on. Even though you are irritated by the word, at least it does have that very distinct and accepted defintion which differentiates it from Islam per se.

I do understand that you'd rather keep away from words with connotations which could aggravate the religious divide - but the term still does obviously describe the reality. The religious aspect is central to their fanaticism - we should be able to be objective and accept that, without sinking into the blanket religious vilification you mentioned.