Well, you can activate SAS in this mission, but maybe it's a not enough precise/advanced SAS ?
In the training scenario about orbital inclination, you can do it with pure normal push for sure.
This is a nice diagram, but I'm not sure to understand what the length of the vectors are in this representation ? orbital speed ? The thing is only direction is important in this maneuver, not final speed, so if I 'm ok to get higher equatorial speed then my actual orbit speed, it will look like you diagram with the red line, right ?