Well I received the part Steve pointed me towards and I was able to modify it to make it work.
The catch that attaches to the top of the door has a pin on the bottom that fits into a hole on the door frame. The pin on this newer part is too small in diameter and a snug fit is required to keep it in place. So I found a small piece of plastic tubing and slipped it over the original pin and it fits and holds great.
The actual catch that attaches to the hinge didn't actually fit at all with either the flat head machine screw that came with the kit, or the original one which is a pan-head shoulder screw. The screw in the kit is 6mm (M6 1.0) and the old screw and it's corresponding threaded hole in the hinge is a M7 1.0. It took me awhile to find a suitable M7 flat-head machine screw (it's super short) but I finally did and after opening up the hole in the catch a bit, it went together fine.
Since I had everything apart and since the original hinges were a bit corroded and the chrome plating was coming off, I removed both top hinges, cleaned them up, and painted them with a silver hammertone
paint. It's a nice, clean, unassuming look. I didn't want to get them re-chromed and I thought silver
paint would look cheesy. So I went with a hammertone finish and I think it looks pretty nice. See pix below.
Thanks to everyone for their suggestions and especially to Steve for finding the image of the original part on that Australian caravan site and for locating the alternate Dometic part. The
fridge is now ready for my trip from California to Alaska which kicks off New Year's Day.