Amelio identified that the clone deal was bad (fixed license cost instead of based on % of machine price) and rebranded to MacOS 8 in order to renegotiate to get a better clone deal.
Spindler made the original clone deals assuming they would be chasing aggressively low pricing as seen in the PC market but instead the clones ate Apple's high-end market, replacing Apple's high-end margin with cheap OS licenses. So Amelio wanted to renegotiate the deals to be based on the value of the machine so that Apple would not lose from a clone maker selling a high-end machine instead of Apple.
Jobs as iCEO continued the negotiations (after all, NeXT was also an OS-only company at that point so Jobs wasn't necessarily sold on the idea that Apple had to sell hardware) but nobody aside from UMAX bit on the more expensive MacOS 8 license (so yeah there was one clone they had a MacOS 8 license - you can find UMAX MacOS 8 CDs out there) so Jobs gave up, and there were no other clones.
Yes, Amelio's departure coincided with the release of System 8 in July 1997. (The NeXT deal and Jobs' return was in February.)
To be fair, System 8 was more than just a service update for System 7: it introduced the Platinum UI, the Appearance API, a multithreaded Finder, and various Copland features. (This was quite a rich update, maybe second only to System 7. It would have been a bit strange to just give this all away as System 7.7.)
Problem was that, for backwards compatibility, all applications ran in a single pre-emptively scheduled task that cooperatively scheduled between them. You could write additional tasks that got scheduled preemptively, but they couldn’t make all system calls (https://developer.apple.com/library/archive/documentation/Ca...)
System 9 was really just about some compatibility layers in preparation for OSX, as I remember it.
(And, yes, 7.6 was a major step in terms of stability. There was also some pre-PPC, pre-OpenDoc version of System 7 that was pretty stable, but with all those major integrations that came with the further iterations, things became a bit "delicate".)
IIRC Mac OS 9.0.x had significant changes for users directly booted into it, as did 9.1 (though to a lesser extent). I think it was 9.2.X that was mostly focused on usage with Classic.
The clones licensed System 7, so jobs took the next version, branded it 8 and forced it out, cutting them off.