tracking my own phone calls

I was hoping someone could help me with this.

I need to maintain a log of phone calls (not voice mails, but calls) sent and received to certain numbers, which are work related, and happen at all hours of the night. This is to show my employer as a measure of work-effort / job demands.

The abilities to do this on an iphone are pretty limited.

iOS is naturally locked-down against this sort of data tracking in a pro-privacy effort, which is great and does make me feel better about my iphone, but it’s not helpful for me in this case.

The best I have now is taking multiple screen shots every night before I got to bed, of that day’s calls. Screen shots of the previous day’s calls are less useful because they all say “yesterday” beside them, and do not give a specific time.

No apps that I have been able to find will track ingoing/outgoing calls and put them into a neat list (again, the user privacy culture).

Using call logs from my wireless provider does not work, as they either do not include the 800 number that most often calls me, or do not include the call if it isn't connected. (The call wakes me up, and causes me to log into a secured website, but I don't need to actually answer the call, so it's not tracked on my last 3 months of calls available to me from Verizon.)

Can anyone think of a more useful method than taking a bunch of screen shots before I turn in every night?

Thank you.