When you say you have to push the reset coil, do you mean the Reset Relay isn't energizing?
On the PSUU (Player-Step-Up-Unit) not resetting, you may want to make sure the PSUU and
Coin Step Up wiper boards are clean and the wipers are making good contact with their wiper boards..

Okay, this is what's labeled as the "Reset Relay"..
There's a set of contacts (9E) that run off of the score motor's cam that breaks
and cuts the the current to the Reset Relay.
Also, is the "G.O. (Game Over) Relay going into the game play mode?
When the G.O. Relay is in the game play mode (game over light is not lit in the backglass),
a set of contacts in the G.O. Relay should open, thus breaking the current to the Reset relay,
but I'd first maybe suspect the 9E set of contacts on the score motor's cam being the issue..
Also, probably not, but does the Coin Relay remain energized?