I've always found that listing the documents someone was trained against in their training log is sufficient. If I list that they were trained against my GMP Policy XX.XX.XX and that policy contains the verification of efficacy within it, it has satisfied the auditors.
What I think OP is missing from the attached sample would be a separate Skills Description of some type. It should be a template describing the jobs/roles within your facility, and what training is required for people who do those jobs/roles. As some examples, everyone needs GMP training; Maintenance people don't need training on your receiving/shipping procedures; Production employees may or may not need training on storage practices (depending on what tasks they routinely perform. So you should have a template register outlining what each role requires for training, then be able to provide a record showing any person in a specific role has been trained on the required items.
It helps quite a bit when you end up with new hires, as production rarely wants to invest hours and hours of training for a new hire who may not last a week. In the past when I've designated that new hires are under strict supervision during their probationary periods, I've been able to justify lesser levels of training to establish the employee will remain which justifies higher levels of training for higher levels of responsibility.