Where was the family living in 1850? Was it Terrebonne Parish or Orleans Parish? I searched, but did not find, a death record for John in Orleans Parish. If he died in Terrebonne Parish [and was Catholic] it may be possible to find a death record there in Father Hebert's books. Unfortunately, if the death was not reported in Orleans Parish, there would not be a record. As I mentioned before, it may be a good idea to get the death records of John's two sons in order to learn the place of birth in PA. Also, the place of birth of John and Martha should also be listed on those documents. They can be obtained at the Louisiana State Archives in Baton Rouge. The charge is $5.00 and the service is usually quick.
Using the info from the 1900 census which shows that George's father, John, was from Washington, D.C., I found that an R.M. Desha [perhaps Robert Mortimer ?] was in D.C. in 1820. What is interesting is that I had already found mention of an R.M. Desha, Louisiana Lodge No. 88, who was a visitor to the Grand Lodge of the Republic of Texas. The meeting was held on Sunday, December 30, 1838. I'm not sure what this means, but if it was a lodge in Louisiana, then I suppose that R.M. Desha lived in Louisiana. I did more research on R.M. Desha and found that he was a paymaster of the U.S. Marine Corps in the early 1800s in D.C. He was apparently well-known and "important".
George's oldest child is Frederick Fulmer and I figured that Fulmer might be a family name. I found two men in PA on the 1820 census named Frederick Fulmer. One was in Bucks Co. and the other in Philly. I found the genealogy of the one in Bucks Co. which dates to Germany about 1700. Mortimer was probably also a family name and there were Mortimers in PA. All this is interesting, but in order to do research in PA, you would need to have a town or at least a county of birth of the Desha children and their parents. Otherwise, you'll just be "spinning your wheels".