Based on some of the other comments and some experimentation, I realized that the Google help text actually implies that forward slashes in the Search field don't need to be escaped (so it's only quasi-regex):
A common use case for the Search and Replace filter is to turn multiple URLs into one. For example, to merge 'example.com/article/CA/planning+your+trip.html' and 'example.com/article/NY/exploring+the+country.html' so that your reports for the profiles for which you will apply this filter will show 'example.com/article/', please follow these steps:
Search String: example\.com/article/.*
Replace String: example\.com/article/
So I was able to create a Search/Replace Filter with the following:
Search String: [^^]/$
Replace String: [blank]
And it appears to be working.