That confirms what I thought... All the machines on which the game plays fine, are between VA2-5 models, which use a EXL-P604 drive, which is the one that can play even the worst discs in my Saturns too (including a broken disc!).
And the ones that don't boot are all VA13 or 15 models, which use EXL-P608 drives, and I've heard people talk about how that one is somehow worse.
The odd one out is the S59000291 machine, which should be a VA0 motherboard, and the oldest machine of the bunch. I've seen the lasers in these fail, so I imagine this one is not-that-tough either. Which drive does it use, a standard JVC one (ENR-007B or D), or one of those crooked, small drives?
This, however, only confirms my suspicion about some Saturns have cd drives being higher quality than others by design. It does not explain why two identical discs do not behave the same. I think there may be some mastering problems on some copies which go below standard user data, but that's purely speculation on my part.