I've made some progress over the last two weeks. I replaced the "organic" tunnel with a plastic tunnel from the Pegasus "Power Plant Construction set":

The aluminum is just bare metal foil and it's supposed to represent a thermal blanket. I may or may not keep it.
In addition to the single porthole in the picture above, I added a telescope/camera port (closed):

The dull aluminum and the shiny aluminum
are the same paint. I bought some Createx Auto Air Colors acrylic paints a while ago. This is the first time I've used this paint and it's fantastic. The shiny aluminum is straight from the bottle (thinned with windshield wiper fluid for airbrushing). The dull aluminum is the same paint, mixed with Vallejo matt varnish and thinned for airbrushing. Easy to mix, easy to clean up and the results are as good as other lacquer or enamel based metallics.
Since it's an acrylic (and compatible with Vallejo, as I found out) you can mix up quite a range of shades.
Here's a picture of the bottle info:

Next I have to add a couple of antennas (maybe a radar dish) and some details. I may redo the solar panels, though.