Today, the new television would be delivered. Last saturday we bought it in a brick-and-mortar store, for EUR 799. This morning, they called that they didn't have that particular type of TV anymore...
I did a quick price check. Turns out that this type of TV has been around for a while, and that it can be had online for EUR 650! And one of the places that carries that model is situated in Beuningen -- just on the other side of the highway that runs behind our house. They also operate a physical store (in a cheap non-prime location) where you can come collect your stuff.
So we cancelled our order with the B&M store (for a full refund, of course), I placed an order on the website of the other store, and this afternoon we walked out with the exact same TV for EUR 150 less.
Now if only I could get audio over the HDMI, and could get the machine to actually show the DirectShow video on the TV, life would be perfect.