This does look very interesting. I'm not sure I see any war imagery though. Could you tell which parts look like war imagery to you? Also, what war would this be about? (It does look Iranian to me, and I don't think there has been a war in the time period where one might guess this rug was woven?)

Hamadan area is quite correct. From north western Hamadan area. Interesting desing, but low quality. It is a typical village rug, probably Saweh. I would divide the design in two parts: the almost symmetric 80% and the rest with the "collums". The remind me pictures of Persepolis with the builing in the middle (might be a tomb).
Colors are a little like some rugs from Koliay / Songhor area. Also the Birds look like in rugs fro there.

The tag tells it came to US from Germany. It was probably sold in Hamburg, the tag tells it went thru customs.

KrowGyrl,
your interpretation of the picture is very ok, and it took me a while also to get the point of the design. Your are absolutely right about the idea of personal experiment. This rug is why I love persien village and nomadic rugs. They are always good for a surprise. The 80% symmetric are where the weaver started, you can tell from the pile direction. Then he or she had the rug almost finished, and for some reason we will never know the second part was added. As rugpro mentioned, for this money it is a great rug for a collection. It is no great quality, but a nice and funny sample of village rugs. And every rug that makes you think or talk about it is worth buying.
I have a Loribaft that has a similar idea, that is why I bought it:

Funny Loribaft rug

Look at the beginning / lower part. The weaver was using a square design, and for ome reason, she decided to do the rest of the rug with circles.

Here's my absolute favourite of this kind: It's a Yahyali and must have been made around the 1920s by someone who was in awe of the Russian propeller planes that could be seen in the sky. This must be a one of a kind rug, and I somewhat regret I didn't buy it when it was for sale. See how the plane and the waving pilot are "floating" in the field, as if really flying in the sky, but similar to the way guls float in 19th century turkmen rugs.

KrowGyrl,
i came from a traditional persian rug family, so my focus was on fine old rugs (Isfahan, Kashan, Qum and so on) at the beginning. In the last years it spread to everything and from everywhere. I buy every good old moroccon berber I can find, every unusual turkish rug and I love persian tribal rugs.
War rugs are also very amazing, and I agree about the difference between the early rugs from the time of the soviet invasion and the commercial rugs made due to the growing collector scene in the west fot this type of rug.
Shereen,
really nice rug, I would have bought it right away! This is what makes rug collecting so great - you always find a rug you have never seen before.