How long are you going to be out of town for? I know the badis don't like it that hot, but I honestly would slowly ramp the temp up to 86 and hope for the best while you are gone. You can't do anything else that wouldn't require supervison. It's likely the badis will survive the high temperature for a short period and you stand to save the most fish by increasing to this temperature.
Edit: Also, treating with salt may wipe out your bb as I have recently found treating my goldfish. So, this is definitely something I would not try while being away. One more thing... 3 cardinals?