I haven't done it (since we don't cook inside right now), so my opinion is of limited value. If I did, I would use a single sheet- stainless steel, pressed tin, or molded plastic, depending on the look I was going for. I would rivet it in place using the existing holes for the top of the lower cabinet and the bottom of the upper cabinet- just slip it between the cabinets and the shell covering and use slightly longer rivets. No new holes and no adhesive.
For myself, I'm not a fan of tiles- too much movin' and shakin' in a trailer.
I saved this photo for inspiration, taken from a trailer that sold
a while back. It uses a stainless steel panel. It looks like the window was removed and reinstalled so the backsplash is under the trim ring, but I'm not 100% sure. It also looks like they bent it to cover the countertop as well, probably since they changed the sink to a different shape. Don't think I would go that far, but it sure looks nice!