Not a pilot ...from maintenance view there are two posibilities how to improve scenario 2 :
Use highest stabilised N1 seting approved by company SOP before pushing TOGA - I remember companies which normally used 60% N1 in such cases.
Ask engineers to improve acceleration on slow engine - old MEC has function for fuel specific gravity setting - it can help, but should be used with caution. Correct (dynamic) riging of VSV can help too.