This is a great question. The answer however depends on whether you have local guidance or procedures established or higher headquarters guidance or procedures established.  The FAR and DFARS do not get prescriptive enough to mandate manual call logs vs using the GPC bank statement.

This is really a contract file content question. See FAR 4.802(d) and FAR 4.803 Contents of contract files. You should also Review AFFARS 5304.803 (note: I tried to review those links but the USAF fire wall would not allow me to view).

But there additional guidance at FAR 13.303-5(e) which states to limit documentation to essential information and forms and at FAR 13.303-5(e)(3) it gives you the latitude on how to document the minimal, necessary information.  Neither the DFARS nor AFFARS implements or supplements this.

Bottom-line: The GPC bank statements could/would be acceptable unless they don't contain the information required by FAR 13.303-5(e)(3) and/or you have local or higher HQ guidance or procedures that mandate something different.