OK. I only describe the second route of Knuckles because Sonic's route should be easy to get. I got every ring of these 6-ring-bunches with getting the big ring before , then I turned into Hyper Knuckles and got into the bonus stage without getting a ring there. Then I turned back and got the second big ring, because you can jump far enough to get the spring. It could have been many more rings if I wouldn't be so slow. I finished this zone in 9:59, so I could have submitted 99900 more points, but this isn't allowed I think... And I wondered why you didn't get all rings.
And BTW, here's why I submitted so quick. There were many, many stats I got long ago so I only had to find the paper where I wrote down those stats.