I created a custom List Bullet paragraph style for my template. I wanted
template users to be able to click an icon and get that style.

So I made a custom toolbar and populated it with the paragraph styles for my
three List Bullet level styles (along with three custom numbered list
styles). Everything works just fine EXCEPT the Level 1 bullet style. Is that
because it's based on a the default (and then renamed) List Bullet style?

How can I get that first level bullet style to work on my custom toolbar?

If you can answer this one, you rock!