For your consideration:
HVAC duct-sealing foil tape (adhesive backing) can, with care and patience, be used to replace the chrome film. The result has a finish that's almost indistinguishable from the original. I used this foil to restore my door cards and rear kick panels. Five years later, the tape remains securely in place.
Steps:
Leave the trim strip in place, but peel off the 'chrome' layer. It comes off as a thin film and you should be able to remove 100% of it without needing to use chemicals. Left behind will be the blue-coloured plastic strip. It has a 'D' cross-section. Measure the perimeter of that cross-section by shaping a piece of aluminum foil over the surface and marking the base of the 'D' on each side with an awl or straight pin. Flatten out the foil and take your measurement. I measured it at 9mm for the rear kick panel. I'm not sure whether it was the same for the door card accent strip.
Cut a length of HVAC duct-sealing foil that's about 6" slightly longer than the door trim strip. Secure it to a flat surface, shiny side up, using regular 'duct tape' at each end. Mark off several strips, using the 'D' perimeter measurement to define the width of each strip. Using a long straight edge and a utility knife (with a fresh blade), cut at least full-length 6 strips (you eventually only need two, but you'll probably ruin at least two at the start as you practice stripping off the backing sheet and then applying to the door strip). For each lengthwise cut, work from the inboard edge of the widthwise duct tape at one end to the similar point at the other end. Then, after making your six lengthwise cuts, use a shorter straight edge to cut widthwise at each end. Tip: It helps if you clamp the long straight edge to the table/bench top, so that it can't move while you're making each long cut.
Clean the surface of the blue plastic trim strip thoroughly. I used denatured alcohol. It's particularly important to get the top and bottom parts of the 'D' clean (where the strip meets the door trim vinyl).
As noted, it takes a bit of practice to figure out how to pull the backing strip off the aluminum foil strip without putting a kink in the foil and/or having the foil accidentally bond to some unintended surface before you have a chance to start laying it down on the intended target (i.e. door card's blue plastic strip). It also takes a steady hand to keep the tape properly centered on the blue plastic strip as you lay it into place along the length of the plastic strip.
The application technique is to lightly lay the foil onto the crown of the D. Press it into place at the front end of the plastic strip, then align while gradually lowering the full length of the foil down into place. It may take a few tries to get this right. Unfortunately, every failed attempt will ruin the foil, so you'll need to use a new strip for your next attempt.
Once you get a good result, the next step is to cut the excess off at the front and rear ends of the foil. You'll need to judge the position of these end trim cuts so that, once pressed down, the cut end of the foil will align with the end of the blue plastic strip. Getting an acceptable result here requires a little additional work because the end of the blue plastic strip is rounded. The foil will not stretch to meet this contour. The only way to avoid a crinkled surface is to make two short lengthwise cuts so that the foil is now divided into three short segments. Eventually (but not now), you'll be able to press the center part down first, and then press the top and bottom segments into place. There'll be a slight overlap.
Returning to the main job, your foil strip at this point is lying flat along the length of the blue plastic strip, touching only the crown of the 'D'. You now start working the foil down over the 'D' contour. Use a soft cloth rub lengthwise, gradually working the tape down over the 'D' contour. To avoid 'bunching', work from the center out to each end, rather than from front to rear. Work from the crown of the 'D' outwards, alternating from the upper half to the lower half.
I think you'll be very pleased with the final result. My only caveat for this technique is that I haven't tested the effectiveness of the foil adhesive under extreme temperatures (e.g. car parked outdoors in the summer with the windows up). If you're concerned about this and think you know of a better adhesive, you could always try gluing chrome mylar film over the blue plastic trim strip. Personally, I like the foil because it's metal and actually bends to into shape over the 'D' contour, meaning that there's very little residual force trying to lift the edges. At extreme temps, the adhesive may temporarily get a bit gooey (technical term), but I don't think the foil will lift unless it's disturbed by the side of your arm. I take some consolation from the fact that this foil is designed to be reliable for use on air distribution ducts that carry both cooled and heated air.