factory ones are viscous, i had my gearbox overhauled some time ago, and mine has got a Mechanical LSD in it now i remember the mechanic telling me it didnt need any special stub axle, its been a while so i dont remeber what was said.
but recoing a box will cost around 1.5k, the 2nd and 3rd synchros are very notorious for going on mr2 so i would def fix them in whichever of the box you choose to go with.
if the box has never been opened before and they say its got some kind of lsd then it has to be a viscous one.
if your going with viscous one its not a repairable unit and once its worn out it has to be replaced. mechanical clutch type ones can be serviced, problem with the clutch type ones are they never are quiet and will shudder a lot if the wrong oil is used in the gearbox, use the right oil for the LSD and the synchros will start playing up and get hard to engage, its a no win situation, so you have to pick one or the other(smooth shifting or LSD chatter) you can get them to a happy medium but involves a lot of headache trying to get the right amount of LSD additive into the Gearbox oil so that it still shifts ok but also doesnt make the LSD chatter. i still havent found that medium yet cause i gave up lol.
 
cheers

Viscous LSD may not be rebuildable, but they can last a long time. Mine was checked 15k ago when I rebuilt my box & it was still fine. 220k kms approx.

Verify that box & search for another IMO.

so the gearbox rebuilders were wrong???, theres no way that box was factory sealed and had that in there.
that looks very much like what i got except my plastic/nylon ring is blue instead of yellow.
the TRD ones chatter less apparently. but i guess that depends on how tight the shims are in the LSD

It probably is a KAAZ (Edit:clutch) unit in there (going by the plates and no hex bar).
TRD is mechanical and only aftermarket AFAIK.

DVST8R has now shown me a photo of his Kaaz LSD, and it looks *edit* very similar. 
 

MR2QIK
I remember hearing a few years ago that there was a TRD viscous LSD available for the E153. From memory, someone took a close look at one & it was pretty much the same the OEM LSD. I wouldn't be surprised if it were a factory fitted option either.
Had a quick poke around & there's a few Gen3 LSD transmissions for sale on Ebay. Didn't look closely @ the terms, but if they can be inspected & somewhat warranted, wouldn't be a bad option at all.

I don't want to keep trying my luck with other second hand boxes, because I'll always want to get them inspected, and unless I'm lucky and find one that needs no work at all, the inspection costs will keep adding up until I find one that needs no work at all.
EDIT: I just noticed that you said "if they can be inspected & somewhat warranted", but I don't want to take that risk.

I've been in close contact with Rob the whole way through, and he's under no obligation or pressure of any sort to purchase the box.
 
The box was advertised as a 2nd hand E153 with LSD. Rob still has the option of returning the box in the condition it was in, without having to purchase. In light of the inspection results, costs and efforts the Rob went to, I offered to drop the price of the box.
 
I'm happy to work through any solution you choose Rob, be it to fix this one up or fix your old box up, and as I've mentioned to you before, should you chose to fix your other box, I'm willing to do a cost price LSD of your choice for your troubles.
 
Just thought I'd clarify in case anyone on the forum thought I was just trying to dump a box on Rob and run away :P

I've just been googling for some comparisons between Kaaz (or other clutch/plate style LSDs) and Quaife LSDs, and I'm starting to think that I should listen to my gut feeling and get the Quaife, and therefore keep my original box. Apart from the maintenance side of things, I reckon I would hate the chatter of a plate/clutch LSD. I don't know how loud they really are, but I'm particularly fussy when it comes to annoying noises in my car, eg. I generally keep my car interiors free of clutter purely so I don't have to listen to (or see) things moving around all the time.

As a few people have said, it would be good if I could get my existing box looked at to verify exactly which part/s have broken before I make a final decision, but after (if) I get that done by my mechanic I may have to leave my car at his workshop for a long time while waiting for parts to arrive etc, and that would annoy him as much as me lol. Anyways, I've contacted the NZ Quaife supplier (and Dylan too) to see how soon I can get a Quaife and at what price.
Whatever is broken in my original box, I hope the required parts are still available and able to fit my early revision box!