Craig,
If you update to SP06+ the base install comes with Tomcat7, this way you don't need to do anything extra. If your Tomcat was installed as part of BOE XI, I would suggest not doing anything as the patches will automatically update your Tomcat7.
The approach mentioned of SP03 to SP05 to SP07 will work perfectly
Also make sure to installed JRE/JRK 1.7 and update ALL the Tomcat 7 related paths and environment variable path
- JRE_HOME=
- JDK_HOME=
Good Luck.
Ajay