This adjustment moved the bar a little, so they are no longer aligned.
"A little"? When I tested it, the heading moved all the way to the right, and that is what I see now after your adjustments. The two are still aligned (on the same line). There is no third black bar that I can see; are you talking about the outline partially beneath the two headings? That is a border for #moduleMenu.

Your solution to the two boxes will be in adjusting the javascript, and you need to ask in the Picadilly Posh template support thread. Anne is good about helping with her templates.
Once the boxes are displaying as you like, the details can be worked out. Have you looked at admin settings for the centerboxes?