I was intrigued by your post because I thought you'd display that the mats actually did add up to 19k despite my initial assumptions that the OP was crazy and asking for way too much money.
Instead you seem to have stopped around 4k for the expensive stuff. The rest, even arcanite bars (which I got for my hammer spending like 3 gold per arcane crystal, thorium costs nothing either) is pitifully cheap. Maybe I would be willing to allow you 1k for all of that stuff bought entirely off the AH, including the few gold per core etc.
Dark iron is, admittedly, a pain, but still not expensive. True, I am a miner and blacksmith myself, but the actual smelting and crafting steps take less than 15 minutes. You can buy someone's time for that. it's not expensive.
At the end of the day, when I farmed my hammer it took me 20 minutes a week over the course of maybe a month. Farming it yourself also gives you a chance to pick up the eye of sulfuras along the way, which is the only reason this hammer matters. If I wanted to try harder to speed up that process, I could have, but 20 minutes a week was nothing, and I spent MAYBE 1.5k getting extra stuff when I already had my eye, and was close enough to having the mats that I just said screw it.
You'll notice that I didn't bother responding to the OP, because hey, if somebody wants to pay 19k for something they can do themselves for an investment of a few hours, that's their prerogative. But I was a bit confused by your method of counting. You get to 4k, toss on a another 1, maybe 2k. Even if you wanted to say those were rock bottom prices, you could potentially argue that 10k is fair, which is what you said you'd pay....
The jump from that to suddenly 19k being a fair price is like...silly, in my opinion. It irked me.