Cardboard headliner

The original headlining you describe is a good enough method - you have to be accurate at cutting if you want to copy it. I've been glueing unbacked autocarpet (usually black) direct to roof for people who want a low cost job that looks good. It depends on the shape of the rails round the roof edge. Most vehicles look fine carpeted despite the factory bumps and hollows normally hidden behind the liner. The carpet needs to be fitted by cutting a bigger piece than required (it comes 2meters wide in NZ) spraying contact adhesive (find heat resistant type) across the carpet piece and roof. Your paint gun will be fine if you get spray adhesive. Car trimmers or upholsterers will have large drum and sell you 1 litre cheaper than you can buy it at the hardware. Take a clean tin with you. Mark with chalk on edge of piece centres, front and rear, and starting in the centre of the roof lay it in by brushing your hand forward and then back. You may need a friend's help for a large panel van roof. Then brush from centre to each side. Corners are last. Hold corner of carpet near roof with one hand and keep enough tension on it to pull out sag from both directions, then brush in an arc across the corner beginning at the centre of roof and working towards the corner. Repeat this in each corner. (Contact glue works when you press it together so you're OK if you touch the two surfaces together by mistake. Just tug it back off)
Unbacked autocarpet is very forgiving because it will stretch and will take to the curves so long as you keep enough tension on it and do it in the order I said. After this you need to glue the carpet on the rail round the edges. Hopefully it will hide under the windlace on the door edges and the screen rubber in front. If not you need to be careful with a craft knife (box cutter)cutting round the edges It looks OK cut raw so long as it is well stuck. So don't be too light with spraying the glue on the carpet. Your second lot of glueing on the rails round the edges will pobably have to be brushed on the body to prevent overspray on the main roof carpet. If you get any on the finished carpet it comes off with white spirits - (Clear Gas) Its better if you can avoid using white spirits on finished carpet because it may soak through and weaken glue underneath. I have never had one fall out tho using this method. Tip - dont buy aerosol spray glue I have found it can't take heat of sun on roof. Have fun and ask if you want more info.