Another workaround:
1. Create the new forum for the resume uploads. Be sure to enable attachments for that forum. Also Enable Full Post Moderation for that forum.
2. Create a 2nd private forum that will house the resumes.
3. Whenever there is an upload to the first forum, you review/approve it, then immediately move it to the private forum.
Technically, the resume could be viewed in the few seconds it takes you to move the post, so just keep that in mind.