Excuses for the delay, but urgent matters kept me away for a few days...
OK, back to business.
The jaggies are most visible on the edges, or, in other words: there where there is a rather harsh transition in tone. So what we can do is blur the edges. That way the effect will be less visible. For the mask we need a greyscale image that hides everything but rather soft "blurred" edges.
The procedure is as follows, and if there is a step you don't follow, do not hesitate to ask, ok? I do not mention shortcuts on purpose. They will come later on, but it is best to first know what they mean, and do. OK, let's go ahead and create a mask.
1/ First open the image you have upsampled in several steps so as to get the best effect possible.
2/ Image>Duplicate This duplicates your open image.
3/ Set the duplicate to greyscale (Image>Mode>Greyscale). Later on, when you have more experience, you may want to use a channel, but for now it is easier to use a greyscale image.
4/ The best way to get the edges is to use the appropriate filter: Filter>Stylise>Edges .
5/ Yet, to have a good mask that hides everything but the edges, we need to invert this. Image>Invert
6/ We want the edges to be more uniform. This we do with the Median filter. Filter>Median (a value of about 2 should be allright)
7/ We also want them to be thicker: Filter>Other>Maximum. Set this somewhere between 3 to 5, depending on your image.
8/ What we now want, is a softer transition. This we get by blurring: Filter>Blur>Gaussian Blur. Take the same value you chose for the maximum Filter.
Voil?, this is our mask. The advantage of duplicate is that you can now compare the mask with the original so that you see what you did.
OK. Now Select>All and Edit>Copy the mask you created.
Back to your original image now.
1/ Layer>Duplicate This creates a copy of the background (your image) on a new layer.
2/ With this layer active, Layer>Add layer mask>Reveal all . Tis creates a new icon to the left of the layer icon, a layer mask.
3/ Alt+Click on this layer mask icon and edit>Paste This pastes the mask you created on the white, empty, all revealing layer mask.
4/ Now click on the icon of the image at the left of the layer mask icon. This makes the image on the layer active. You can see that it is active because you'll see a brush icon to the left of it.
5/ Now use Gaussian blur on the image on the layer. The image itself will blur but only theoutlines as dictated by the mask will pass.
When you are happy with the settings, save, and then flatten and use save as to save a flattened copy.
Not ideal, but it does lessen the effect of jagged edges a bit.