It appears that the soldier applied for land, patented it, and then his widow applied for land and also patented it. That is a bt odd, which may explain some of the reason you haven't received all the files.
Did the soldier also serve in the Georgia militia? There may be two men with the same name who served unless he rendered multiple terms of service. There is a pension application under that name.
You may need to hire an independent researcher to perform some research on your behalf. There are many names on NARA's researchers list. You'll need to find someone with experience researching the War of 1812, and land records.
There are two Pleasant Stathams but this one enlisted in the US Army from Virginia and served 5 years. He was married to Polly. The other was his nephew, served with the Georgia Militia and was married to Nancy; I have his pension file.
I do know that the first Pleasant's land in Arkansas was sold for taxes. As far as I can tell he never lived there and, in fact, was deceased by the time his land was put up for public sale, something I understand was a common occurrence in Arkansas territory at the time - taxes would be levied, due and the land seized before the out-of-territory landowners could receive and respond to the notification.
Hiring a researcher isn't an option. Would these records be available at one of the NARA regional centers?
The records are not at the regional facilities. Best of luck to you.