And this is where the confusion starts
Hate to tell you this 4doorGTS but I do believe you have got it exactly the oher way around

Have you ever opened up one of those gearboxes?
Yes. All 4A-GZE engines came with a E-series gearbox (Stronger gearbox than the C-series, neccecary for the torque the SC engine delivers)
And yes, LSD was an option on the E58. So having an E58 is not a garantuee that you have an LSD gearbox!
The flat piece with the hole is the LSD equiped E58 gearbox.
The rod belongs to the open diif in the non-LSD gearbox.
Some pictures to make my case

:
(These pictures are from my own site, and from my own projects.)
On the right side, we have an open diff (non-LSD) with the rod, connecting the gears.
On the left an Quaife aftermarket ATB LSD (helical)
Now before people start shouting: Yes, these Diffs are from a C52 gearbox. (I opened mine up, revised it and swapped the diff. for an Quaife ATB LSD.
But I can asure you, that the open diff in the E-series trannys have the same built up as the open diff in the C-series (thus with the rod).
If I remember correctly (But I'm not completly sure about that yet. Will be when I have opened up my E58). Toyota put helical LSD's in their factory gearboxes aswell.
Here is a cut through of a helical LSD:
As you can see: no rod but a hole.
And even if they didn't use helical LSD's but friction type LSD's. Here is a pic of such a LSD aswell:
Again: No rod, but a hole
Now I do know that models may vary from different manufacturers and such. But the overall lay-out is mostly the same.
As for the axles...The picture I posted earlier in this thread is from my own E58 gearbox witch I believe has a factory LSD.
Now I do have a picture of the drivers side axle, but it's hard to tell from it. But this has the above mentioned 'shorter' splines:
So these would have come with the LSD gearbox. I know this sounds weird as you would think the longer splines would be more sturdy as the splines give more surface to distribute the load.
As I'm typing this, I am thinking that this might not be true.
The splines are mechanically more likly to break or twist, as the solid centre is smaller in diameter over a bigger lenght (and splines do not provide radial strength). So the axles with the shorter splines can probably handle a bit more abuse as the solid diameter is bigger. (Just thinking out loud, have no way of proving this offcourse.)
I'm wondering if the countersplines in the gearbox are longer aswell with the longer splines or that they are not fully used, in witch case it would be a weak spot.