Hi , 3.08 LSD out of HT will be course spline but HX 3.08 will probably be fine spline. The only trouble is the LSD part will more than likely be worn out . if you have 2 spare axles , put the axles in each end of the diff head ( you will need helper) firstly when you turn the axle both should turn at once. Now put a long bar in-between the axle studs at each end and the helper holds the bar stationary and you try and turn your end , if there is little or no resistance it is stuffed . If it is really hard to turn and you can feel real resistance it should be ok. hope this helps Mark.

3.08 and 2.78 banjo centres have a long attachment bolt on the bottom (when fitted to the diff housing), the other attachment bolts stick out of the housing and you do up the nuts. Check that your current one has this (it should have if you currently have 3.08). Then the HT centre will fit straight in and all you will need is new gaskets and the specific oil for that LSD (different I think from modern LSD oils).

Sorry I don't know about the interchange for HX, but you might run into width issues (for axles if retaining ht diff housing) and if a HX sedan/wagon diff won't be able to fit whole diff due to leaf springs v coils

HX may still be coarse as the change appears to be in 1976. You could get new axles made. Remember the HX one would need work anyway as it will have a6cyl yoke in it. They break easily so keep one for spares. I’d sell them as Torana guys pay stupid $ for them and you’ll get enough for them to get a better diff.

If you bust an LSD banjo, which is probable in a HK-HG sized car with even a standard 253 I'd do this:

Keep your eye out for a Camaro or 6cyl full size Chevy with the same 10-bolt. These whole rear ends turn up from time to time quite cheaply. Get Holden ends put on it (scavenged from a HK-HG banjo housing) and also the HK-HG leaf spring plates off a banjo. The diff you want is a pre 1970 8.2" 10-bolt, out of a Chevrolet. The Pontiac/Olds/Buick diff looks different. See here:
https://www.chevyhardcor...ivetrain/10-bolt-chevy/

You'll have to get some new axles made but these aren't all that expensive, maybe $1200 or so for a pair.

New posi centres and gears for them are pretty cheap:
https://www.ebay.com/itm...AOSwkvdaYD14:rk:31:pf:0
https://www.ebay.com/itm...AAOSwd0BV4LwK:rk:6:pf:0
https://www.ebay.com/itm...AMXQgJRRAhny:rk:10:pf:0

Then either find an original HT-HG 308 Salisbury rear axle (pretty sure this was the light bronze green shaft, 54.42" long) to replace your pink tail shaft or make one out of a V8 HQ one.

That or find an original HK-HG 10-bolt, but you'll still probably have to get axles made as they are 10x harder to find than the diffs themselves.

You'll also have to muck around with the brake hose a bit as it is attached at a different point on the body for the 10-bolt, but you can buy replica brackets for a HJK-HG for the diff end:
https://www.ebay.com.au/...AMXQSnVRbVwz:rk:10:pf:0

I know you'd do another type of diff cheaper, but this is "factory" fitment for a HT, just not with the 253 engine.