The metal behind the board is the psu, as you can see from this shot from behind the case:

The distance between the card and the psu surface is approximately 4 cm when the card is straight:

There are actually two metal clips with a hole, sticking out from the psu (the top one is visible in this picture):

Now that I'm thinking about it, the optimum solution would be to use these two clips and build some sort of support against which the card could lean. Remember that the card always leans toward the inside of the case. The one place where the card can safely lean on something is the black plastic strip between the memory connectors.
This would appear to be a good solution, since the card could still be removed without having to remove the support. Maybe I could even make it so that a fan can be pointed downward along the card, instead of the 80mm can you see in the pics being pointed "kind of toward the card". Observe the professional use of zip ties to hold the fan :-D