A friend sent me a link to this. It's on Github or however that's spelled and I tried my best to find the executable, and finally gave the link to my wife who found the program for me. So, for those of you who are interested and don't want to fiddle with Github, here's a public Dropbox link. I'll leave it up for a week or so.
This program no longer works, so I've taken it out of Dropbox, thus disabling the link. I suppose Google killed his way of working with YouTube. Very sad, but probably inevitable.
Or, an NVDA-addon that someone wrote! Here's the link: https://cloud61.de/index.php/s/TBnTN3T8X2KCQ3m And here's how it works. Just place yourself in your browser on a YouTube video. Then, you can use NVDA + y to convert to mp3, and NVDA + shift + y to download as mp4. NVDA + control + y opens the folder where the downloaded videos are saved, and that keystroke works from anywhere of course. You can't set the location yet, but if you can open the folder with the above mentioned keystroke, you just move it to where you want to have it. I think that's so cool, since it's just one keystroke! And then just open the folder and move it, but that's it! I used Elten before, and that was good, but this is even better, and then, I wouldn't miss out on that if I ever left elten. Don't worry by the way, even though the website suggests German, the addon is in English.