Comment out the if statement that checks whether the action is the first NLA track when it is pushed down, so the influence of the edited action will always be keyed on the first frame if it's not 1.0 whether it's the first NLA track or not.
This was a request from Brad Clark to help bring consistency to the behavior of the NLA. Right now the code was second guessing, overriding user settings. This caused users to not know that the behavior was different or working for other actions pushed down that were not the first one.