I think the fundamental disconnect is about how Joomla migrations occur from 1.5 to 2.5. To get to 2.5, you build a completely new site. If the JUpgrade utility works for you, which I have never gotten it to work, the new site uses tables in the old DB that have a new prefix. JUpgrade may, potentially, migrate the CiviCRM tables. I have never gotten it to work, so I can't comment.
The other method is SP Upgrade which only does:
Articles (along with their Sections and Categories)
So that leaves you with all of your CiviCRM data stuck in an old DB tied to a 1.5 site that you are replacing.
Unless someone has a better idea, the only path I see is exporting all of the data from the old and importing it to the new.
Am I missing an easier method?