I currently have all four rear seat bolts with heads broken off. A previous owner when removing the seats, apparently broke all the bolts, then ground down what remained and covered with bed liner. And the remains of those four bolts are fused in good and solid. Earlier today I tried the vice grips approach from underneath with no luck.
I think the only way you will get the remains of the bolt loose, is by applying a lot of heat to the nut from underneath, and then crossing your fingers the bolt can be moved using vice-grips or preferably some bolt extractor similar to a nut from underneath.
For my part, I am going to carefully cut off each of the captive nuts from underneath, and then install new bolts with regular nuts. Because I don't think anything is going to get enough grip on the underside portion of the bolt to allow removal given the corrosion. I'm rooting for you though, if you manage to get that bolt extracted more power to you.
(Photo below shows the remains of bolts under vehicle, but there are no bolt heads above to wrench on.)
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Oh man, I feel for you! I thought my day was bad with one broken off bolt. Tomorrow is another day, I am going to cross my fingers and hope for luck. The good news in my case, is I don't see any rust on the underside, as in your pics (sorry). My Jeep has only very little rust (garage kept Texas Jeep) and none that I see on the bolt and captive nut.
More to come tomorrow.