I am not a Boeing guy but the concept is generic.
By the end of the 3rd segment (level acceleration) Maximum Continuous Thrust would be selected. The Maximum Engine Out Acceleration Altitude (beginning of 3rd segment) is thus defined by the TOGA time-limit.
The Engine Out Acceleration Altitude can not be lower than 400ft by design (ref: ICAO doc 8168) however most companies have a company default which then becomes the nominal minimum. When there are limiting obstacles for a specific runway which infringe the nominal Level Acceleration Segment (3rd segment) you may find that that the EOAA is increased above the company default, but it would need to be a serious increase for the EOAAmax to become a factor.
As the others have pointed out: a 10-min TOGA limit could increase RTOW in the case of an extended 2nd segment, i.e. limiting obstacles infringing the company default EOAA leading to an increased EOAAmin. I expect this to be the case only from very specific runways with high density altitude.
PS: the 1.2% is the final segment/4th segment, which is based on Max Continuous thrust anyway, so not relevant in this context.