Do you still measure a short when you disconnect the playfield from the rectifier board?

Note: one G.I. wire is connected to ground at the rectifier board, the other G.I. wire connects to the transformer on a very very low resistance winding. The "short" you are now measuring might just be through the transformer G.I. winding which is normal.

So disconnect the playfield J1 connector off the rectifier board and remeasure for short circuits across the playfield lamp socket quadrants (presuming you've separated the quadrants from each other).