In average condition, these things sell for $300-$600 regularly, especially in Japanese auctions under the X1 model number.

In regards to this, I'm personally much more interested in acquiring an LD-S2 over an X1. I'm also curious as to how much rarer the S2 might (if at all). It seems like it would have been harder to sell in the North American market.

If there was one within driving distance, I'd probably commit to one. Other than that, I might as well save the cash and spring for the X0 and its red laser glory.

I have seen LD-S2(LD-X1) and I now own HLD-X0. If the cost is no issue, HLD-X0 is a better player. Some claim(including Kurtis) LD-S2 and HLD-X0(noise reduction off) has same picture quality on NTSC laserdiscs. I do not agree. Although they are close on noise levels(if not same), HLD-X0 has better colors which LD needs, no smearing and better tracking due to red laser. With noise reduction turned on, there is no competition. HLD-X0 can clean any laserdisc from noise without losing detail or bad artifacts.

On good mastered late era discs(super ntsc) i.e. lost in space, titanic, starship troopers, LD-S2 is identical in noise levels and sharpness(all processing OFF) HLD-X0 has better colors. For example on LD-S2 or similar CLD-97 you can count the shade of skin tones in say 10s or 100s(depends on mastering), on HLD-X0 its at least 100s of shades to 1000s. I would say overall HLD-X0 renders colors somewhere between %20-30 better than any other LD player.
I don't know what kind of video processing you have in mind but I doubt that you can find one better than one in HLD-X0. Hands down it has the best video noise reduction. 3D comb filter is also among the best. You can find its equal but don't think you can find one better.

There's more to the X0 than just the S2 chassis it's built on. The red laser, obviously, for one but the X0 NTSC processing was also updated. A description of this from substance I found:

I believe Substance has said the same thing and he’s one of few members to have some hands on time with the higher end machines and also the context necessary to pass onto us his findings. The returns diminish extremely efter CLD-97 in the opinion of most.

I’ve never seen either of the big suckers in action but with the amount of post processing people are using now I don’t know why much of this matters so much. If you have better processing than any of these players had (which is totally possible nowadays) then all you’re really interested in is the most noiseless chassis you can afford to plug into your $4000 magic box or even Kuro for that matter. There really is something to buying older more analog decks and just using the straight composite into modern stuff as opposed to clinging to what was state of the art 20-25 years ago.

The players that fully digitize the image looked amazing at the time on contemporary sets but after my two better decks died and I had to fall back on a lowly 503 I then made new settings on my set (XBR960) after that and to be honest it looks better with subtle sources now than it used to running a 99. Super vivid stuff, digitally remastered in the 90s, not so much, but those LDs that show older analog sources the best like Tokyo Olympiad or 2001...I’m enjoying these more now with the rattly old deck with no digital outs than I was with the self-cooking CLD-99.

Can NR be turned off on CLD-959? Is it identical internally and in performance to CLD-97?

I’m enjoying these more now with the rattly old deck with no digital outs than I was with the self-cooking CLD-99.

I can relate to this. I do, however, wish I had purchased the CLD-97 instead of the 99 from Bayview. At the time (mid 2000s), the 3D comb filter was much more important to me. Now, I just run composite out.