AP Divs for overall layouts are NOT the way to go.
As you have discovered when you attempted to center your layout, AP Divs are removed from the normal document flow and will be LOCKED in place by your parameters while the rest of your content flows all over the place to accomodate viewports and user controlled text resizing etc.
SSI's (Server Side Includes) are a better way to manage repetitive code that appears on many, if not all pages such as headers, menus, footers
So no template? Use a SSI for the header, menu and footer and then add the content to the individual page? And put all these elements into layers and then position them with CSS?
As far as not using absolute positioning, could I work everything up using the AP Divs and then somehow wrap them in a container div and center that container? Is there a way to do that? Could I wrap the divs in a table and center the table?
As Ken already told you, APDivs are not suitable for primary layouts. Work through the following 3-part tutorial. The methods shown apply to either Fireworks or Photoshop generated designs.
Taking a Fireworks comp to a CSS Layout in DW
Part 1 - Initial Design
Part 2 - Markup preparation
Part 3 - Layout and CSS
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Would this at least be better than using tables?
NO. APDivs are not a solution. They will plague you with inconsistent x-browser results and layouts that fall apart when text size is increased in browsers. Start over with a pre-built CSS Layout that has all the columns and containers required for your project. See DW Starter Pages: