Unclegrumpy, read the post from the link you gave and I would just leave it but it is getting stiff and don't want it to start cracking. I have it hanging on a wide shoulder hanger and think I need to slightly stuff the sleeves because they are starting to crease. Before I do anything I will contact several people one being, Shenkursk and get some additional advice.That is a beautiful jacket!
I would stop where you are at as far as putting anything more on it. The suggestion to not fold it is a good one, and the paint looks fine. One problem with putting something on top of the paint that is for leather is it can get under the paint and actually start to loosen it. The museum people sometimes carefully use a clear preservative over the paint. It is to help the paint stay on, not to help the leather. But you have to consider they are preserving for longterm display, not wear...and they have years of expertise and the highly specialized products.
As far as leather products that have silicone, binding agents, mink, coconut or neatsfoot oils...or anything made for new leather...NO! If you have lightly used some Picards, then stop there. Remember, this jacket has made it all these years and is in nice shape with minimal care, so you don't need to do anything.
The "what to put on old leather" is an age old debate. Many of the people on this Forum regularly wear their 70+ leather jackets, and in that case you do need to keep conditioning them. However, most collectors err on the "do nothing" side of the equation. Read post #9 in the thread below. The writer is one of the leading collectors and dealers in high end military items in the US, and is a frequent appraiser on the Antique Road Show TV Show. He is a very nice fellow, and I think would happily answer your question...but it is pretty clear what his answer will be.
My youngest is a big history buff (like my husband) and understands the history of the jacket and knows it's not for wearing. I can't imagine someone wearing it and then losing it. As far as the name patch, if there was one it was stolen along with some of his medals and other items when his house was broken into 20+ years ago. But there isn't any markings on the jacket like there was another patch or name tag on it. But I will ask him when we have lunch later this month.