Original procedure was to hit TOGA at 40% and stable, the second step produced much better results. Especially fewer exceedances. When I left we had been doing it for about 10 years with excellent results.
Different engine acceleration may be a variety of things. JT8Ds were bad for that as they always seemed to have different bleed configurations between the 2 engines.
The big difference with the second step was to get above the minimum RPM for the PMS to start doing it's thing.