I think all of the above answered your question but I will put it in other words.
QW 423.1 itself has the answer you need regarding base metals. However the filler metal F-number is dependent upon those applicable rules.
For GTAW, a welder may be qualified for welding 304 to 304 using 308 by using A-106 to A-106 using 70S-3 since both F Numbers are the same (F-6). For SMAW, the F numbers are NOT the same and an additional test would be required. based upon QW 423.1, the base metal specified in the WPS may be substituted as indicated.
So for GTAW, you don't even have to refer to the P-8 WPS since both base and filler metals are included. For SMAW you would have to use a WPS with F5 filler metals but could substitute P-1 materials as allowed by QW 423.1
However if you want to test the welders using P8 with matching filler metals, you can.
Have a good day.
Gerald Austin