Sad to say, nothing goes in directly.
But you are on the right track.
Something with an F or G series diff will be both stronger and have more chance of finding an LSD.
LSD for T series diffs is very hard to find.
LSD for F and G series diffs can be found through any decent 4WD workshop because they were both used on Landcruisers and the Hilux (aka 4Runner, Tacoma).
My own Australian spec '77 liftback is now using a Japanese spec MA45 Supra solid rear axle with a T series LSD and disc brakes.
It's slightly wider than the standard rear end which gives better handling but required the guards (fenders) to be pumped out a little for the 225x15 wheels I was using.
An RN25 pickup from the early 1970's has the ideal width and a very strong G series diff shared with the Landcruiser. Huge range of ratios available. Comes with 10" drum brakes. You will need to cut off the leaf spring mounts and have the 4 link mounts from your original axle housing welded on. Have a professional shop do it because high accuracy is required and the welding distorts the housing, needing special care to straighten it again. But now for the fly in the ointment - RN25's are very hard to find nowadays.
Luckily, you can do the same thing to any of the later pickup rear ends but you also have to have the housing and axles shortened. Changing the mounts + shortening doesn't cost much more than just changing the mounts. The wheel bolt pattern will be 5x114.3mm. This would go hand in hand with the famous Corona RT132 strut + LN106 pickup 4 spot calipper + Peugeot 5 stud vented disc upgrade
The Landcruiser rear end can be used but it is asymmetric (diff is over to one side).
Shorten the long side so that the diff is in the middle.
Cut off the leaf spring mounts and weld on 4 point mounts.
This is a G series diff - unbreakable but quite heavy.
Heaps of ratios and LSD available through 4WD shops.
IRS is a bit harder.
The Supra IRS is all attached to a K frame and that is bolted to the chassis rails at 4 points.
Unfortunately, Supra and 77 Celica chassis rails are too different.
You can still do it but you need to put some outriggers on the chassis rails so that the Supra K frame can be bolted up.
Since all the rear end forces go through those 4 bolts, the outriggers would have to be extremely strong and attached to the body and existing chassis rails extremely securely.
Needless to say, high accuracy is required or the car will drift sideways.
You also need to cut off the panhard rod bracket because it interferes with the IRS.
Or you could cut out the entire '77 rear chassis rails and surrounding floorpan and replace the whole thing with the Supra IRS rear floorpan and IRS.
Lots of expert welding required.
Last option is a Nissan Skyline solid axle from the late 1980's.
Same wheel bolt pattern as the Celia (4x114.3mm) and has disc brakes.
The Skyline housing is asymmetric.
Again, shorten the long axle.
Cut off the old suspension mounts and weld on the mounts from your original housing.
See the Nissan speed shops for ratios and LSD.
As an extra, any new rear end that has disc brakes will need the rear brake line restrictor removed (drums require much less pressure because of their self servo nature).
A little browsing here might help too.
http://members.iinet.net.au/~stepho/diff.htm
http://members.iinet.net.au/~stepho/celprod.htm#cel29pr
http://members.iinet.net.au/~stepho/celfaq.txt
So, no easy options but at least there are options.
- Stepho