If you weren't in the Nether, then a simple solution would be to fill the volume completely with water. But that's not an option here since water cannot be placed in the Nether. Instead, we'll have to do what we can with solid blocks.
First of all, note that the spawn area is wide but not very thick: it is only 3 blocks high, centered on the spawner. So if you fill those three layers with blocks (the top and bottom layers could be slabs if you want the final result to be small, and the middle could be hollow), then you're done. In the picture you show, this would mean just adding more slabs (or full blocks) all around at the same level as the slabs you currently have on top of the spawners.
If you want to still be able to walk through the volume, I can think of two tricks:
If you place a lower-half slab, and an upper-half slab two spaces above it, then the space between them is 2 blocks high so you can walk through it, and yet only the middle is actually empty air. Therefore, any monster 2 or more blocks high cannot spawn in the area; of the ones you list, only small magma cubes are small enough to spawn, and they're much less dangerous.
Place a checkerboard pattern of wooden fences and nether brick fences. They won't connect, so there will only be single fenceposts and you can walk in the space between them. Cobblestone walls can also be used in this kind of way, but because they are thicker you can't move between two diagonally adjacent ones.
Doesn't work: You could fill the volume with open fence gates, or doors. Or at least I thought you could — testing (version 1.8.7) shows that they now allow spawning.