This is a very common issue and there is no easy fix. The best place to start is often the internet applicant rule and implementing good data management techniques. This limits the data the company needs to capture. Having a process for accepting and reviewing resumes is equally important. For example, reviewing only those resumes submitted for a specific position of requisition. Some companies have an auto-response that includes language about collecting demographic information with self identification forms. Of course, those involved in the process need to follow these processes as strictly as possible. Ultimately, though, the data must be captured in order to comply with the regulations and there is really no way to do this efficiently.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.