You're definitely barking up the wrong tree. If your class files are in their proper location under WEB-INF/classes - or in a JAR in WEB-INF/lib, every JSP in the webapp should see them just fine. That's the way the standard is defined.
As for any other webapp, no. Webapps are supposed to be self-contained. They can't share their toys If you want to share a class between webapps, you have to put it in an inherited classpath such as the server's classpath, which means CATALINA_HOME/lib or someplace like that. Or it may be off CATALINA_BASE. I can never keep the two straight, since usually they're the same place.
Anyway, welcome to the JavaRanch!
Sometimes the only way things ever got fixed is because people became uncomfortable.
It sounds to me like you were using the <Tomcat Home>/webapps/ folder as the ROOT path, and placing all your data in there. This is a nono. Your ROOT path should be: <TOMCAT HOME>/webapps/ROOT/.
Why? The Root path (that you get to like http://localhost:8080/) is the default Context. But any folders put in the <Tomcat Home>/webapps/ path will be considered a NEW Context and so will need a new WEB-INF folder (and will have trouble talking with servlets/jsps/sessions in other Contexts). Each Context is considered a new Application.
If you want all you folders to be part of the same application then you should put all the folders in <Tomcat Home>/webapps/ROOT/. Anything that should be a different application should be in a different folder under <Tomcat Home>/webapps/.
Later, I decide that in addition to my main application listed above, I have another, INDEPENDENT application called accounting which I access through http://localhost:8080/accounting/accountHome.jsp. Because it is a new application I need to make a new directory under <Tomcat Home>/webapps/ and give it a new WEB-INF directory. accountHome.jsp should be in <Tomcat Home>/webapps/accounting/accountHome.jsp accountHome accesses a JavaBean to get some data. The Bean should be in <Tomcat Home>/webapps/accounting/WEB-INF/classes/<package>/AccountManager.class