Normally the nano has 30720 bytes of flash available; the uno has 32256 bytes of flash. The uno exists in two versions: either with DIP or with soldered PLCC as the nano has. 

So why not flashing the bootloader for an uno on it..?!
For a howto for flashing the bootloader see

From now on, in the IDE you have to select the uno for programming the (ex)-nano, and you should tag/label it as "uno" too.