It may be possible to use a nut splitter to break off the nuts saving the original carriage bolts. Not the new style but the old style. You can buy a vintage “Nutsplitter” by H.K. Porter on eBay which is what I have. I have used it numerous times on my truck. The cutting edges on the tool can be rotated so the tool can be inserted between the channel. I looked at my truck and the tool and it looks like it will work.
That's an awesome tool.

I saw a few of them just now on eBay, and it also highlighted H.K. Porter bolt cutters, which might be able to be used as a nut splitter, assuming you have enough room to fit them into the space and for the handles.
I used to be able to cut nuts off bolts with a cutting torch and leave the bolts usable. It's been years since I've tried that, so I might be a bit "rusty".
