This may then be a problem you will only get to overcome fully when you have an opportunity to upgrade to 14.1 or higher. I found the following defect that had been reported on 13.2 and 13.3 which appears to not be possible to reproduce in 14.1+ anymore, and once resolved via upgrade could be giving you the result you were after:
CLRT-73843 The "Clear" button in a portlet filter, clears the content of a read-only field
Steps to Reproduce:
1. Go to the project list
2. Through Actions > Configure, go to the List Filter section > Fields
3. Go to the properties of any field on the filter section, let say Manager
4. Set a default value, enable it as Required in Filter and Read-Only in Filter
5. Save changes and get back to the project list
6. The Manager field contains a default value, it is required and read-only
7. Click on the Clear button.
Expected Result: The manager field is still filled in as it is read-only and the filter action works
Actual Result: The manager field is blank and an error is thrown if filtered: "All required fields need to be filled out"