I haven't done this type of updating, but have one suggested approach. Remove the fabric and foam only and scrap the plywood to a clean, level surface. Pre-build replacement panels using new 1/8 lauan plywood, foam and fabric. You can cut each panel to fit around overhead cabinets, etc prior to putting the foam and fabric on. Use spray adhesive for the foam and fabric. Then attach each panel to the existing panels with construction adhesive.
I've had good results with construction adhesive, there are some "instant grab" waterproof types at HD and Lowes that dry clear, intended to attach shower enclosures to studs or sheetrock. For vertical applications, no temporary bracing is needed, but you certainly will need bracing for overhead installation. And you may need to use the strongest adhesive available regardless of cure time. Just use a very smooth flowing type.
Finally, you will need 'H' trim at panel edges and small crown molding at the sidewalls.
Larry Day, Texas Baptist Men volunteer
'13 Silverado LT 3500HD D/A CCSB 2wd, custom RKI bed
'11 Crossroads Cruiser 32MK loaded