I would stay away from integrally padded covering materials. Due to the way you need to treat seams and so on to create the compound curves you want, the added material will interfere strongly as you manage the selvage edges and extra material.
Have a look at how Henk’s leather covered IP’s manage the surfaces of that complex form.
Consider that you never want to see an unfinished edge. You will be sewing through two layers of heavy material and depending on your seam choices four or more if you are bringing three elements together
You will want to acquire an industrial sewing machine, Juki or similar. Craigslist would be a good source. This is an example:
https://grandrapids.craigslist.org/hvo/d/industrial-juki-ddl-8700/6455752491.html
Try to find one with or buy a guide foot for the machine so that you can more easily make consistent seams, particularly if you want a French seam or similar. The selvage edges on the underside need to be managed, you may want to make allowances in your surfaces for that extra material to live in under the show surface, by this I mean actually making depressed areas in the foam/fiberglass elements for the material to sit into.
Modern cars use injection molded self skinning foam, in mold vinyl fabric or vacuum forming the sheet good to apply the finished surfaces that we see. Depending on the surface you may be able to get away with draping with glue and then wrapping but as the surface becomes more complex you need to add seams to get the conformal surface you desire.
As you are developing your forms I would have some automotive grade vinyl sheet around to start visualizing how you are going to deal with the finish. For some of it you may choose to use a spray on material like Rhino liner to give a UV stable, finished surface that has texture to avoid having to upholster the entire interior and give an appropriate surface to touch. Coordinating the sprayed and upholstered elements will be tricky.
Creating the foam surfaced parts will be the easy part of this job...Just wait until you start making patterns and sewing them together, that is the real job.