Hi RogerQ - If the hinge pins were worn, then you would see the sections of the hinge moving when trying to lift the door at the door handle end and not where the hinge plate attaches to the A frame. But, as you describe ‘movement between the door hinge and the chassis”(?🤷🏼♂️), it is likely that you are correct about the hinge fixings needing tightened.
The carpet around the A-frame just inside the footwell is glued on........when I had to tighten these nuts, it needed a good pull and the use of a flat metal lever to separate the carpet from the frame. But, as that’s the only way in, it’s a good idea to have a can of strong carpet adhesive spray on hand when you’ve done the nuts. There are plenty available on the usual online stores.
I’m not a carpet fitter, but, as long as you generously coat both surfaces that are to be stuck together and then WAIT a few minutes for the glue to get really tacky before pressing them together, the carpet piece should go back OK.