I had a new rod ready to go - 3/32" coated steel from the welding supply shop. (I have another hobby besides pinball, but Shhhhhh!)
Bending the bracket holding the rod so that the rod was centered better did the trick. Had my dad over to play, and he was not subtle in his nudges. No tilting.
Adjusted the contacts on the pops. They fire much easier now when the ball is above the pops. On this game, you need to be able to work the ball back up to the top, so that's working much better.
All that's left to do on the machine is raise up two inserts and figure out why one of the flippers wants to shudder some. And maybe tinker with the slope. I still haven't been able to get the specials lit "Blow Your Top!". Must be too much slope, but I'm going to give it another week or so of play, now that the pops are more sensitive.