Hi Tim, I have this plant too. You got your plant from the same place I did--Hausermann's in Chicago. Good job re-purposing pop bottles. You have good drainage on these new pots, right? The roots you uncovered are not very healthy, usually they become that way when they get inconsistent watering.
Our plants originally came from SE Asia. They are terrestrials and live on forest floors. These plants are considered intermediate temperature plants--they don't tolerate high temperatures nor too cold winter temperatures. They like bright filtered light. If you can grow an African violet, your Paph will flourish. I have mine growing in a window on the west side of the house.
Your potting medium is okay for now but you might consider getting a mix of sphagnum moss, fine fir bark, perlite and charcoal. There is an online vendor called Kelly's Korner Orchid Supplies (
Kelley's Korner Orchid Supplies, We offer everything to grow great Orchids!) that sells a mix specifically for Phaps & Seedling. You can purchase mix like this from other vendors.
You have discovered how fragile your Phaph's roots are, your plants' roots have experienced root rot. It is hard to tell which roots are vital and which are dead. The plant will recover if you water regularly and allow the plants' roots to dry almost completely--do not let it go bone dry. Water throughly. Keep your plants where air circulates freely.
As winter approaches and the temperatures get colder, avoid the three horsemen of orchid death: cold temperature, wet roots, and stagnant air.
I hope this helps. Here is a picture of the potting media I mentioned. That is a Nickel coin.