Thanks for replying! Do you like the Companion? I haven't used mine yet, but it looks like it should fit a fair bit. I love the personal stories and history that are connected to these bags (and lucky you for scoring the book too!), I wish I knew more about who owned mine. I'm hoping to use as a hybrid bike bag/purse, so lots of time at the farmers market and library.I have this exact bag and had similar issues. For the piping I used a leather adhesive "shoe goo." It is intended for leather shoes but worked just fine. I put some just slightly inside with a tooth pick, gently pressed the leather back into place on the piping and allowed to dry after washing the bag, of course.
For my bags that did not take the conditioner as well, I am currently using a polish to help re-establish some color and evenness. The only bag I have done this to is a Macdougal in "tan" with Kiwi polish. It turned out really well and looks so much better. I have sinced ordered some polish from amazon in colors that will suit the other browns in my collection, including the companion. I believe the color is "tabac" or medium brown if you look at polishes to match.
Good luck. I love this bag and managed to score it for only $12 on ebay from a man and his wife who carried it for decades as a purse then camera bag. Even came with the original booklet. I will try to post photos when mine is done, hopefully this week.

I have Shoe Goo in the house, so that's a great recommendation I can try soon! Can I ask, is Kiwi polish the exception to shoe polish on bags? I see a lot of discussion about the challenges of removing shoe polish on this thread, but I know there are different brands and ingredients.
I'd love to see your rehab when it's ready!