SOA is actually pretty easy to understand.
The main thing you are trying to do is keep the die from overheating. What makes the die overheat? Power, watts.
The three things you need to be aware of (and who's relationship is shown on an SOA curve) are voltage, current, and temperature.
The thing that makes SOA confusing is that the device has a max value for each of those things, but that max value is given INDEPENDENT of the other values. What this means is that, for some fictional device that has a max current of 10A and a max voltage of 100V, you can only realistically get 10A at really low voltages or run at 100V with really low currents. You can't run at max current of 10A and max voltage of 100V at he same time.
So what the SOA curve is showing you is the relationship of the current and voltage you can run continuously AND keep the die temp within limits. If you want more current, you have to drop the voltage. More voltage, then drop the current. It's all about the watts, because it's the watts that are heating up the die.
Now another thing you have to be aware of is the temperature of the package. Remember that what you are really interested in is the temperature of the die, which is always going to change temp faster than the temp of the package. If the package is already hot, then you have less room for more heat so you can't have as many watts going into it. What this means is that you need to derate the SOA curve based on the temperature of the device, or lower the running temperature.
That's pretty much it. The SOA curve is just letting you know the combination of amps, volts, and temp that will keep the device from overheating. One more thing to watch out for though is that you won't get much of a warning if you exceed the SOA curve. The device will just overheat and blow up. Because of that, it's a good idea not to try to run right on the edge of the given SOA. Give yourself some headroom.
If you are looking for a good device to run in a linear application like this(as opposed to switching which is what most FETs are made for), a good place to start looking is the Audio industry. They are the guys that are primarily pushing the high SOA linear operation devices at reasonable prices.