ZAP: Mix manual browsing, active scanning and fuzzing for testing a very large Web application?

We've got a very large Web application with about 1000 pages to be tested (www.project-open.com, a project + finance management application for service companies). Each page may take multiple parameters (object-id, filters, column name to use for sorting, ...). We are now going to implement additional security checks on these parameters, so we need to systematically test that a) offensive parameter values are rejected and b) that the parameter values actually used by the application are accepted correctly.

Example: We might want to say that the sort_column parameter in a page should only consist of alphanumeric characters. But the application in reality may include a column name with a space in it, leading to a false positive security alert (space character not being an alphanumeric character).

My idea for testing this would be to 1) manually navigate to each of these pages in proxy mode, 2) tell ZAP to start spidering all links on this page for one or two levels and 3) tell ZAP to start fuzzing on these URLs.

How can this be implemented? I've got a basic understanding of ZAP and did some security testing of ]project-open[. I've read about a ZAP extension for scanning a list of URLs, but in our case we want to execute some specific ZAP actions on each of these URLs...