PROGRESS! ...Sort of.
I gave the dip switch reset one more try, then went for a sandwich. It went back to green and flashing blue for about 15 minutes, then switched to the rotating lights I was expecting. After resetting the switches to 11111 and rebooting, everything came back!
So, to resolve this, do the following:
Power off your Pineapple. Disconnect the ethernet cable (this is the one major change I made from my last few attempts). Set the dip switches to 10011 (from left to right). Turn on the Pineapple. Go get a sandwich. Wait for the lights to start cycling with a steady green light. Power off the Pineapple. Reset the dip switches to 11111. Power on the Pineapple and let it boot.
Unfortunately, I'm now seeing other issues, but I AM able to get an IP again and get back into the interface.