It might be a good idea to take a step back, and start from scratch. Ignoring the solenoid voltage flip for now, let's get the power to your dash sorted out, since that will give us a foundation from which we can branch out from.
Unplug your R/R (which may or may not have a failed component in it causing weird grounding issues) and with the ignition off, check that you have voltage on both sides of your main fuse. If so, then turn your ignition to 'park' and you should get tail-lights and you should be able to turn on your hazards.
If either one of those things can turn on, then your main circuit for power through the JB is OK. If both of them fail to come on, you've got a connection problem in your battery/JB/harness. If only one of them works, you've likely got a bad ignition puck (each of those uses a distinct switch in the puck, unlikely to both go bad at exactly the same time).
Switching to 'on' causes the ignition puck to re-route your tail-light through the headlight fuse, so you can see if that circuit gives different results than the more direct wire used when in park.