Don't assume you need to replace your refrigerator. You may have dirt, spiderwebs, or other critters blocking the airflow, or propane flow.
If you have a manual light unit, it may just need adjustment or a new thermocouple to keep the propane on. These appliances are common to all RV's so you won't necessarily need an Airstream mechanic to work on it. It's a lot less expensive to repair the old one - so at least get an opinion. Many people have working reefers that are older than yours.
Hey, I'm glad to meet someone that "coastal" like me. You may also find that Colonial Airstream in NJ can advise you on your refrigerator. They sell a LOT of Airstreams.
Hope you don't have any of the dreaded tail droop on your Airstream.
If you ever head down toward Virginia Beach (recommend OCTOBER - beautiful and most of the tourists are gone) give me a holla!
Today is a gift, that's why they call it the present.