When soaking I would let the container of water slowly come up near the top level of the bark. Living in Florida you might have a challenge keeping your phals in bark? I don't know this personally, but I have heard that with all the warm weather in your area it could be challenging - you will potentially have to water more than those of us who live in cooler climates - but be careful not to overwater too - note the skewer method that is noted in this forum. Eventually, if you continue to grow phals, you might want to experiment with another media or two with your phals - so far it sounds like you are doing the right thing. If the humidity stays up to descent levels your damaged roots should quickly grow back. After 4-5 times of soaking your bark you will probably be able to just pour a good quantity through and the bark will retain an acceptable quantity? If you continue to soak the importance is to occastionally run lots of water through to wash out extra mineral accumulations. Some people like to add a few drops of Superthrive (root stimulant) to their watering - especially when a plant needs some help in recuperating from previous use. The extra pot size at this point is going to depend upon your expertise in watering accordingly - sticking a bamboo skewer into the media where your roots are at will help you determine if the center of the pot is adequately dry to prevent additional root rot.
On the subject of cats, I have all my mother's cat chewed orchids - they look like they have been through a war! :-) As orchids grow rather slowly it takes many years to visually recover from this kind of battle - from which the cats always win.
Good luck and enjoy! mike