I purchased my new furnace for my 310 online from Adventure RV. My 310 is a 1982, the direct replacement furnace is a Suburban NT-30sp. Exact same measurements and duct placement. They are available online from many many RV supply dealers.
I didnt realize that Airstream built a 310 in 1987 as your post states. The '82 310 also has only one furnace, 30,000btu. Good luck on your project.
If you scroll down in the link you will find what years Airstream made the 310 motorhome. You may want to double check your documents, or maybe the 1987 310 in your original post was a typo. I believe the last year that the 310 model was produced was 1984. Having the correct model and year in your inquiry will have a good deal of importance as to obtaining the correct furnace for your motorhome.