It actually got warm enough today so that I was able to jack up the front end of the car, drain the differential oil, and replace it with the Castrol Transmax.
I guesstimate about one and a quarter quarts of old oil removed. It was very dark red-brown to black in color, but at least the differential was still reasonably full, and there is no evidence of leaks or damage to the differential case, so that's a good thing.
There's a little magnet about a quarter inch diameter in the end of the drain plug. It had a tiny little bit of super-small metal particles attached to it which suggest to me that the differential is still in really good shape.
I managed to put 1/2 cup (or maybe a little bit more) ATF into the differential than I drained out. I just stuck the small end of a funnel into a 2 foot piece of clear vinyl hose I had laying around, and that worked great for filling it.
I did not buy or install new aluminum crush washers on either the fill plug or the drain plug, but I cleaned all the surfaces well with brake parts cleaner and I torqued the bolts down tightly enough so nothing is leaking. I will check again for leaks the next time I work on it (which should be in a few days) but I don't expect any leaks since I've always had good luck reusing these types of washers.
BTW, if anyone is interested, the fill bolt is 17mm which I removed from below with a flat ratcheting box-end wrench. But the drain plug requires a 10mm Allen wrench which I did not have, so I made a trip to Harbor Freight and picked up a set of six 3/8 inch drive metric Allen-head sockets on sale for six bucks. The 10mm was the largest in the set and it worked perfectly.
Also note that I removed the front driver side wheel/tire which made it easier for me to crawl under the car and reach around to where I could access the fill and drain bolts.
So far so good. My next task will probably be to drain and fill the power steering fluid, then when the transmission oil pan gasket arrives I can replace the transmission oil, too.
This car doesn't burn any engine oil, but it does leak a little bit at the valve cover gasket ... so replacing that gasket is another little project I'll be doing soon.