I was actually seeing two issues. First, I'd get the timeout error. Secondly, after the user inputs the last of the variables the popup window would lock their Commcell Console access until the script completed (which would usually take several minutes).
The first part was solved via a registry edit called nWFRESPONSETIMEOUT . I just increased it and I haven't seen an issue since.
The second issue with the popup window locking the session I had found a less than elegant solution. After the input popup I inserted a simple alert-style informational window. Just so it looks like it serves a purpose, I have it display a "Job is now starting" message, but really it kills the popup box and frees the user to work on other things as the workflow is running.