Why does Signaltap insist on recompile after recompile?

If you've already done a full compile, you shouldn't have to do what you're doing. Even if it says to start a rapid recompile, have you tried connecting to and programming your device, using the .stp file as is? Is the option to use the .stp file enabled in the project settings (Assignments menu -> Settings)?

If you want to avoid accidentally making changes that require recompilation, turn on one of the lock modes in the .stp file window.