It's a shame you didn't use the old trick of heating and cooling the bolt.
Removing rusted bolt basics
One of the first jobs I ever had was at a shop doing full on restorations on vintage Fords (we specialized in model 40s 1933-34). By boss taught me MANY things I use every day. One of them was the best trick for getting rusted bolts out that I have ever tried.
You need your torch with a small tip.
Take the torch and make a perfect flame like you are going to weld. Heat the bolt head up till it starts to turn red. (If the bolt is already broken off you will need to saw a grove to use a flat blade screwdriver or have enough to grab with locking pliers) Then quickly cool it with a squirt bottle of water. Repeat, heat it, then cool it. Do this a number of times and the bolt WILL turn right out. If you can, heat the nut around the bolt right before you try turning it out, BUT DON'T HEAT THE BOLT. This will expand the nut from around the bolt. I have did this on Model A door hinges, if you are not familiar with them, it is a 5/16 bolt with a little flat blade screw driver head! A ridiculous design that rusted in to tight to remove around 1950! You can imagine how hard they are to remove in 2000. I have did these with total success, only needing a regular hand screw driver about 99% of the time.
The way I figure the heating and cooling expands and contracts the screw breaking it loose from the rusts grip.
Now, that plate, I believe it's a "cage nut" which means it's caged in there and you will have to drill out some spot welds to remove it. It may even be between two panels and you would have to take the whole pillar apart to remove it.
Let's look at another way to solve this problem. You can carefully grind the broken off bolt down flush with the plate and then drill the bolt out with a smaller drill and re-thread the hole using a tap.