Technique for "organic" pads?

You have missed a few.
 
Korg Wavestation. One of the most beautiful synths for complex pads. The plugin IS as good as the hardware.
 
New Sonic Arts Granite. An amazing granular synth. Can turn any sound such as a single tabla hit into the most amazing pads I have ever heard.
 
Check here for example:
https://www.youtube.com/watch?v=MuN0Jezi2Kw&t=339s
and here too:
https://www.youtube.com/watch?v=qhIPcKB7eug
 
This is one complex instrument. It takes a while to master but when you do you can unleash its power. I love it. You can tune the pads too and yes it is still connected to your controller and playable from a keyboard. The sounds all transpose up and down etc..
 
Sound Guru The Mangle. Another amazing granular. I have this too and also love it. Despite being granular too like Granite it is very different beast. Listen here to what can be done from a single Tibetan bell hit:
 
https://www.youtube.com/watch?v=UFDg7X3dlfc
 
Iris 2 is amazing. I have got it and the sounds definitely do not sound all the same. It depends on who is driving it. I agree about the price tag too but one day it was on special for $49.95 I think. I bought it. There is a huge library that goes with it too.
 
Be careful about using sound libraries that come with all the complex pads already made for you. Everyone else has them too. Make them yourself.
 
Listen to Eno's Ambient 4 On Land for the most organic pads ever created. He started it all.
 
I also have a Roland JD800 synth too and if you spend the time making sounds they can be still out of this world. Be prepared to build pads yourself like using many tracks. Effects do go a long way too. Long reverbs etc.. 
 

+1 for Korg Wavestation and Iris 2. Those are the only two mentioned above that I familiar with. The Wavestation is basically the brains of the original synth with all add-ons, while Iris 2 is a lot deeper than the presets may appear at first (incredibly capable actually). The sale point is valid for both of these, iZotope is pretty regular with theirs.

I cannot speak to the others, so the above comment is not to discount the validity of them.

What distinguishes "organic" from "synthetic" sounds? In one word: "complexity".
 
Sounds that originate acoustically in the natural world are naturally complex by nature. Look at the lengths developers have gone to make sampled pianos sound natural, replicating small factors such sympathetic resonance, damper noise, release samples and crossfaded velocity layers. And the piano is actually one of the easiest acoustical instruments to fake, as evidenced by the plethora of piano libraries on the market. Still, it took many years to get to where we are today.
 
Synthetic sounds, by comparison, are much simpler in nature. You start with some oscillators whose only contribution is static harmonic content. Then you modulate them in different ways to effect what we call "movement". What we're really trying to do is make those oscillators less boring. But we have to go to great lengths to get anything anywhere near as complex as an acoustical instrument, because LFOs and envelope generators suffer from predictability. You'll give a patch some nice variation only to realize it "varies" way too consistently and ultimately becomes boring.
 
Why is it boring? Because our ears are trained in the real world. Complex sounds are what we expect. We crave something new, even if that newness only occurred in the last half-second. Want great-sounding pads that aren't boring? Make them change moment-to-moment. It's not enough to layer multiple sounds. Layers have to be independently moving. 
 
Start with complex waveforms. Strings are a good foundation, because they are inherently complex, harmonically-speaking. You have to start with harmonic complexity, because without that you have no basis for variation through modulation. You will never make an interesting pad from just sine waves (although sines can make for an interesting component layer). Make sure each layer adds something distinct to the mix.
 
Amplitude modulation is the simplest, and arguably the most effective technique for movement. Make each layer slowly fade in and out, each at a different rate. This continuously gives the ear something new to zero in on. Filtering is the next-easiest. Slowly sweep a high-pass filter, again with a different LFO rate and waveform for each layer. Comb filtering is especially good for constantly shifting focus, especially when each layer is modulated independently.
 
Not all synthesizers are created equal when it comes to modulation. Some are capable but don't make it easy. Some simply don't provide the internal connections. Any synth that limits you to just the basic oscillator waveforms is going to be a challenge to make interesting pads with. Wavetable synths are better, sample-based synths better still.
 
This is why Omnisphere is the king of pads. It has it all: classic waveforms, gobs of wavetable waveforms, sampled sound sources, sophisticated layering and modulation. And a ton of high-quality effects. But you don't necessarily need Omnisphere to create great pads, just multiple and varied sound sources that weave in and out of the mix. You don't need to get it all from one synth, either - for example, I like to blend Kontakt-based strings with U-he Zebra for a mix of organic and synthetic that is neither.