Go ahead and use Stability if your medication doesn't say to avoid it. It may work, and if it does it will be beneficial to your tank at this point. Follow the instructions.
Replace what salt you take out in each water change. So a 50% change will remove half the salt (15 tsp), in 30 gallons of water for your 60 gallon tank.
Use prime in large, frequent water changes, at a double dose. This will detoxify most ammonia and some nitrite. The salt will greatly help with the nitrite.
Continue the meds as described in the instructions. If they mention specifically when to perform water changes, then do as it says. If no mention of water changes is made, then use your best judgement and try to keep parameters (ammonia and nitrite) under control.
Remember that just like a 50% change will remove 50% of the salt, a 50% water change will remove half of the ammonia, nitrite, and nitrate in the aquarium as well.
Does that help?