I believe this same issue was causing me problems immediately after I built my Egg-Bot. Once I completed the build, I hooked it up to my computer, and tried to start drawing via a sample Inkscape file. the pen arm would just flop to the side, and the pen head would just jump up and down. I don’t know if I got more than one issue going on here. I will re attached the shaft collar to the wooden part, and hopefully this will fix the problem.
You mentioned super glue. Does it matter what type, thin, thick? Would epoxy be a better choice?
I would love to give the grandson an Egg-Bot egg for Easter tomorrow. This is great fun!! ( Although I’m entertained easily).