Although the other answers here may be useful in some respect, overall they are incomplete.
I did find a way to resolve my problem and get rid of this error, though it does not quite accomplish the cascading system that I had hoped for.
It seems that dsh was right in that my issue is the difference between the classpath used by eclipse as it compiles my code, and the classpath used at runtime by tomcat. Or more specifically, the DAO jar file exists within my project, but doesn't get deployed to the tomcat server.
To solve this, I went to my Project's Properties > Web Deployment Assembly > Add... > Archives from Workspace > Add...
I then selected the DAO jar and added it in. The project then built and ran fine, without the NoClassDefFoundError. So my problem was solved, essentially.
However, I'm not sure what would happen if I changed/updated the jar files in the Core project.