Dynavector XV-1S ---is it overkill for my system?

It is not overkill. You will hear a definite improvement with the XV-1s. However, the lack of easy VTA adjustment in the Classic 1 tonearm limits your ability to fine tune playback for different slabs of vinyl, which the XV-1s will readily reveal. Still, for whatever weight record you choose to adjust the arm to, you will get improved results over your current 17D3.

Clearly the contrarian here, I continue to say: the Classic table and tonearm are competent units and you will hear an improvement with the XV-1s. Are there better tonearms than the Classic 1? Well, yes. But it is certainly competent. As is the turntable. If you upgrade the table or preamp, you'll not outgrow the XV-1s and, in the interim, you'll have better results than the 17D,

And I agree that if you improve the phonostage, you'll hear more of what the XV-1s delivers. (I'm assuming your current phonostage, which I don't know, is at least able to deliver the gain needed by the XV-1s.) If you later upgrade to one of the top tonearms, you'll hear even more of what the XV-1s can deliver.

Bottom line, I think the Classic 1 turntable is certainly a good enough table and arm combination to allow the XV-1s to perform a up to a fair degree of its capabilities. I've heard it in systems with less capable arms than the Classic 1.
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