I just spray some penatrating oil like PB blaster into the tube where the frame end cap goes in. Then, I use a piece of wood wedged against the edge where it enters the frame and pound it out gently. If you get oil in there and let it set a while, it should eventually come out. There are clips that hold into the frame on some of those pieces. Make sure you push them up and in when backing out the end caps.
I never thought about putting a rod all the way through the frame and punching them out that way. If you got something long enough, that sounds like a good plan as well. But again, penatrating oil is your friend, no matter what method you use. That rust really freezes things up, even with plastic on steel.
As far as the lid hinge bolts, I had one that did the same things as you and never did get them out. The cook box must have had a serious melt down since it was bulged, so, I didn't try too hard and never did try heating them with a propane torch which might work for you. Hopefully the pins are stuck in the end caps and not the cook box itself.
I have a silver C in my inventory and that will likely be my first project coming out of the gate in the spring.