Your assumption is incorrect. The exams are valid for the issue of a CPL and/or an IR for 3 years from the date of gaining a pass in all of the required examination papers. The fact that you already hold an ICAO licence is not relevant.
Having had the CPL and IR issued within the 3 year validity, the exams remain valid for the issue of an ATPL for 7 years from the last validity date of the IR. In other words, provided you do not let the IR expire by more than 7 years, the exams remain valid indefinitely.
The 7 year period does (can) not apply unless and until you hold an IR and, therefore, the critical period is 3 years to have that issued - in your case, I assume, as part of the ATPL.