How to remove chair with no access to bolt heads underneath?

Thanks for all the great suggestions. I ended up doing what DougE suggested and figured when the bolts dropped into the sub floor I could squirt some expanding foam down there to trap the bolts and keep them from banging around. Turns out, there is apparently some rigid insulation in the subfloor that is keeping the bolts from dropping all the way down. Win-win! However, after doing two of the bolts, I cut the carpet back to expose the other two and they are installed the opposite direction! Why would they do this? The nuts are on the bottom, and are not captive (I checked to be sure). So I guess I'll just have to grind the head off the other two bolts.

DougE appears to have the best solution.

Good suggestions. How about retightening the nut.Then drill and tap a hole in the center of the bolt. The screw head must be small enough for the nut to pass over it. Then make an eye using a length of thin mechanics wire and fasten the loop under the small screw and tighten the screw. Now you can loosen and remove the nut by holding the bolt with a screwdriver as mentioned above. Now let the bolt slide down the hole until it clears the bottom and move it to the side of the hole just far enough so you can fit a very small drill down the hole to the bottom and drill a hole through that. This will give you the location of the hole on the subfloor and once you have that just drill it bigger so you can drop the bolt by using the mechanics wire through the bottom hole. Just be sure you don't drill into the propane tank.

I use a tool called a "nutcracker". Check it out.

Use a hacksaw to cut a slot in the end of the bolt. Hold the bolt with a screwdriver while you turn the nut with a wrench.

Are you sure there is not an opening allowing access with a special wrench? Or some way to access by removing the propane tank container? Or drill a large hole up to access each head?

How do you remove nylon lock nuts?

Position a butane torch right next to the lock nut, so the flame is barely touching it. Hold it in place until you smell the nylon in the center of the lock nut beginning to melt.