Dear Eric,
As i understood you are having two problems.
1.If after activation of Billing and Goods Movement in my in-completion status groups--still why system is doing these activities'
Ans: if you activate these(Goods issue &billing) two checks in Status groups---system check for the relevant fields in-completion(Example--Without picking quantity PIKMG--can not be done the subsequent document--in this case PGI)(Without payment terms-ZTERM-- Billing cannot be done)(these two are internally hardcoded in the program of in-completion)--You are maintaining these two fields--so system allowing you.
Note: Please press F1--on these two fields in status group--your doubt will be clarified further.
2.What Idocs you are using standard or Custom one?
As i understood that your picking will be confirmed by Idoc and you want to restrict the PGI-If your Idoc is custom one--If the field ANZPK missing--Why dont you try to keep the required ANZPK by default in your Idoc--itself.
Hope i catch your point.
Phanikumar