Err, why? Because I don't agree with your physics defying premise? Did you review those posts showing how your premise is incorrect? How do you explain the perspective difference when you move closer or further away from a scene (as opposed to a flat or virtually flat object?)
Maybe no insult was intended but it did come across rude in the circumstances given I was trying to help you understand your misunderstanding. As a former CAD Operator I'm surprised you do not have a better understanding of the matter, or were you specifically meaning a flat 2D object as opposed to a normal 3D photographic scene, or even an object designed in CAD? How do you relate your theory to the differences between Isometric projection. Oblique projection, Perspective projection and Orthographic projection?

I think Algi just got out of bed on the wrong side this morning! I'm not sure I follow any of this parallax business when discussed in relation to SLRs / DSLRs as opposed to TLRs and compacts as it isn't a problem.

Don't bin them as they're classified as hazardous waste, send them for recycling.

To prove that isn't the case, imagine being somewhere in the Scottish Highlands with a gorgeous sunset you wish to capture featuring Ben Nevis as you just happen to be staying close by.
However you find yourself in a location where Ben Nevis is completely obscuring most of the sky, let alone the sun. You take a photo anyhow and then decide to drive somewhere a bit further away so you can see both Ben Nevis and the setting sun. You now get your photograph as Ben Nevis is no longer that close to obscures the sun. But how though could those two images ever be the same no matter what lens you used? In this instance you've moved further away not closer but I'm sure you wouldn't argue that is the reason for the difference?

I wondered that too but the Sigma website was proving less than helpful. Perhaps others can do better with it. Its strange that some of these seem to work OK and others do not.
As to the dock, you may well be right. As to getting them fixed I don't thinks its Johnsons as they're not Pentax lenses, but back to Sigma themselves. Maybe get the mount replaced at the same time? Mine's all OK so I'll leave it as it is.

If some work and some don't, it sounds like those that don't are knackered.

With one of these: http://www.ebay.co.uk/itm/Sigma-USB-Dock-UD-01-PA-for-Pentax-Fit-Lenses-/3618618...
As to whether updates are available for the lens I cannot make sense of the Sigma website to find out, it partly runs on flash and I have that disabled (why on earth these days when I thought it was obsolete.) Maybe someone knows!

Just tried my Siggy 150-500 on the K1 following the alert here. It all works just fine.

I doubt you'll find any ultra wide angle without any distortion. By definition it's inevitable as it's outside the normal field of view. In real life photos though (as opposed to a test charts) I doubt you'll be aware of anything amiss.
To top it all, you don't want to pay more than £400 so the Samyang fits within that easily, I believe the Irix would double that. If you paid £4000 I doubt it would be free of distortion which makes the Samyang a true bargain for what it offers. As I asked, what distortion needs correcting in that image I posted?
Manual focussing of an UWA is not a problem given the huge depth of field, indeed AF is overkill.
Another option might be to explore the Pentax UWA's, eg the K or A 15mm f3.5, or the K 18mm f3.5 which might just come in at about your budget.

Samyang 14mm photo just taken for you

(Note: The exif shows 15mm as the K-1 doesn't offer 14mm as a manual lens focal length setting.)
What distortion correction does that need? (I think you're thinking of the 12mm fish-eye, but even that can be corrected with hemi-fisheye.)
The Sigma 12-24mm isn't particularly sharp. OK for web images but not a patch on the resolution of the Samyang.