I tried to add a super.updateComponent call in the right spot
No where has anybody suggested that you add "super.updateComponent()" in your code. Read the suggestions and don't make up code.
Is overriding paint just bad style or would it cause any of my problems.
It is bad style and will potentially cause problems if done incorrectly. You have implemented it incorrectly and are having problems.
You where given a link to the Swing tutorial that contains working example. If you can't understand the working examples I'm not sure how you expect us to help because we can't write the code for you. If you don't understand something from the tutorial then you need to ask a specific question.
The tutorial also has a section on "How to Use Swing Timers" which can help you out.