Is paralleling diodes a bad idea?
If you put a low value resistor, for example 1 ohm or 1/2 ohm, something like that, in series with each diode, and then parallel those assemblies, the resistors help to keep the load even between the two diodes. If one diode starts to take more of the load current (as it would with thermal run-away), the IR drop on the resistor lowers the voltage for that diode, tending to push the current back down.

The resistors need to be rated for whatever I^2*R loss they incur, and this usually means multi-watt ratings. Fortunately this sort of thing is typically only encountered in power supplies, where the inductance associated with wire-wound resistors isn't a bad thing. It's generally not a problem to find 0.1 ohm, 0.25 ohm, etc, in 5W, on up.