This exploration shows us that we could get a spectrum similar to that of an LED by having several closely spaced energy levels. When we look at the spectrum of an LED, we see a broad spectrum with no dark regions in it. So, atoms in an LED must have many energy states that are extremely close together. No real gas has the energy levels to create this type of spectrum. We can create it only on a computer with our "unknown" gas. So, we must look beyond gas atoms to explain the spectra of LEDs. This conclusion is not surprising because LEDs are made of small bits of solids.
Solids have many atoms that are close together and interact with each other. These interactions create very closely spaced energy levels. In addition to having energy levels which are very close together, a solid has an extremely large number of levels - literally billions and billions. Because of the large number and the close spacing we treat each group as a band of energy level. When you tried to match an LED spectrum with the Emission Spectroscopy program, you created something similar to an energy band with just a few levels. A solid may have several bands of energy. However, only two of the bands are involved in light emissions. (So, it works just like the model you created with closely spaced spectral lines.) The band with the highest energy contains electrons that cannot leave the solid but are not firmly attached to any atom. They can move throughout the solid. This freedom of motion allows these electrons to carry (or conduct) energy through the solid. So, we call this band the conduction band.