Ditto the Sunbeam Specialities recommendation. That is where I got mine. It is about 1/2 inch thicker front to back than the OEM one. But there is sufficient room in the slip joint at the trans end for the shaft to go in the extra distance and still have enough fore and aft movement slack.
You will probably want to dress the part of the shaft that until now has been outside the tailshaft seal but in the future will be inside it. Smooth it out so it does not tear up the seal as it rotates. Mine had gotten pretty rough in that area over the years.
I has my LSD professionally installed, which I expect you will be doing as well. My guys are also a Spicer distributor and were mystified at the part number on the flange I got from Sunbeam Specialities. It is not a good number from their perspective, not a part they could get. They would have been able to sourse a fine spline flange but it would have been twice as thick front to back as the OEM one. That could have caused problems as a result at the trans end, possibly requiring the drive shaft to be shortened. Anyway, the flange from Sunbeam Specialities presented no problems.
I expect your LSD is the correct one that will accept the coarse spline OEM axle shafts. If not, you will need to replace those too. Sunbeam Specialities has them.
I expect you are having all new bearings and races and seals installed as long as you are putting in the LSD. Good idea after 40+ years and as long as you are there with it apart for the LSD install. A word about the somewhat soft metal in the OEM axle shaft and hubs. The threaded shaft ends are subject to being mushroomed when they try to press out/pull off the hub from the shaft. The shaft ends are tapered and after 40+ years are usually mated quite tightly to the hubs. (Apparently the shaft ends on the American version of the Dana 44 are straight, not tapered, and come apart a lot easier.) The equipment pressure on the end of the shaft can fairly easily mushroom the ends and then the threads have to be restored. Not a cheap process. Or you replace the shaft entirely, also not cheap. An old Shop Notes trick is to spin on a thread chasing die (not thread cutting die) onto the shaft end before trying to pull/press off the hub. Then once the hub is off, they can just back off the die and straighten the threads as they go. Beats having to argue with them over who has to pay for fixing the problem if it occurs. Wish I had told them to do that. I have a reconditioned shaft if you are interested...
BTW, the shop also managed to slightly bend one of the hub ears in removing it from the axle. Enough that I could not get the wheel on. I ended up putting a 1/2 water pipe over the lug bolt and tapping the pipe cautiously with a heavy hammer several times until I could get the wheel on.
Hope some of that is helpful!
Cheers, Gene