Old neutral safety switch stuck to shaft

I have a 2005 automatic V6 and got a p0705 code. Also had the gears not light up on dash while shifting so I bought an aftermarket neutral safety switch. Went to remove the old (broken) one and it's stuck to the shaft. I've tried heat and penetrating oil and can't get it to budge. I broke off where the bolt threaded on, on accident (picture with flashlight) but I don't think that changes much. Short of pull my cat to fit a drill in there and drilling the old one I don't know what to do. Any help would be appreciated.


Edit: got er!

First thing to do is chip off the four teeth you can see missing in the photos above. Then if you can drop the cat it'll give you more room. Otherwise just drill through anywhere you can fit close to the shaft. Use a small bit and increase size until you tear up enough of the switch to pry it off. The goal of this is to get the housing off, the metal sleeve will remain. Then heat the metal sleeve as much as possible and use a small wood chisel to chip off the bottom of that metal sleeve. If you can get that off, heat it all again and the rest of the metal should pop right off. You will inevitably knick the steel shaft while doing this but as long as you don't gash it too bad that's okay. The new neutral safety switch will not want to slid on, so sand the shaft until it slides on easily. This will likely take a while. You shouldn't force the new one on, no more than a few light taps and wiggles. Once you have the new nss on, coat the plug in dielectric grease and plug it in. Then put the top bolt in but don't tighten it all the way, same for the bottom nut. Have a buddy put you shifter to neutral, then turn your key to on but not start, obviously, so you can still see the dash light up with what gear your in. Shift the nss back and forth until your buddy tells you the neutral light is staying lit on the dash. Bolt er down there and you should be good

 

Very common for that to happen due to the switch being aluminum and the shaft being steel, typically they have to be cut off carefully with a dremmel or something similar.