Welcome to the club. I think I've seen those red posts come up before either in the seeking-parts-thread here or on everyone's favorite auction site. The tape and shims are likely because they've shrunk slightly over time and no longer fit snugly in their holes.
One of the neat features of this game is that if you can bump the middle, purple bumper it will return one completed ball from the trough to the player by dropping it into the ball lift trough. If you look closely you can see that the bottom of the ball trough is split into two sections. The whole bottom slides out of the way at the start of the game but the smaller section slides out of the way when the purple bumper is hit.
Dan previously found me offline I think through my Champion web page (https://www.funwithpinball.com/resources/1939-Bally-Champion) which is a longer version of the topic (https://pinside.com/pinball/forum/topic/1939-bally-champion) I started here a couple of years ago.
Now I'm curious how many others are still out there.
/Mark