Morning Denny! The older headliners are also cardboard...but heavier. IMHO I don't think that they will flatten out and remain that way after you put it back up. Getting it down without it falling apart will be a victory in itself!!!However, it doesn't cost anything to give it a try.
I've used tempered masonite (Home Depot@ less than $10.@4x8 sheet) on several other vehicles.
If you place a wet rag on the back (rough) side of the cut-to-fit piece,hang the area to be bent off the edge of a table and add weight gradually you can easily make a 90 degree bend with a 6" radius. I put a c-clamp on the outside edge and hang weights off of it as the bend increases. You want to do this in stages as hanging too much weight too quickly, can break the masonite.
Be sure to weight the part on the flat table. It
usually takes a couple days of keeping the rag wet and adding weight to accomplish the curve. Let it dry up overnight and you'll be good-to-go in the morning. I like to cover it with velour...cuts down on cab noise.
However, I'm going to go a little different on my 54 Chevy. Instead of a 2 piece that's split across the cab, I'm going to use my "cheapie" cardboard replacement liner as a pattern to split the headliner into 3 pieces. Two...one each side of the cab that will be fixed and one in the center that can easily be dropped. Thinking about adding some gadgets and forming an overhead console.
This would require scrapping the cross-cab metal stiffener and adding a front-to-back aluminum stiffener, pop riveted on top of the windshield and rear window lips. Alan H. and I kicked this around in an earlier post so for the sake of brevity, do a search and you can get some more info from it.
If you have questions you know how to get in touch. Feel free!!