Okay, so you only got the first ten off the ski slope. There's 50 up there and you can reach them all.
Moreover, you should be skipping over the boss and not under, you'll gain 14 more rings. That's gonna come at a cost of retracing Knuckles' path a little bit. Ask Flying Fox for help -- I showed her how to do just that (partial screenwrap technique).
Lastly, there are 3 rings embedded in the wall at the end. To acquire them, equip your Lightning Shield, and go over the ceiling of the level, spin-dash-flying and landing onto loops in between. Jump down near the end of the stage, before the small gap where 48 rings and a special stage are -- consult the map.
By the way, fantastic job. You're doing what many TSCers should have strived to do long ago. Best of luck to you on earning the championship.
Oh, and hey, if you want to ask about any of my ring stats and there's not a .giz recording somewhere, let me know. I'll explain them to the best of my ability.