I've also been working on the first example. The result attached.
1. A level adjustments layer was used to turn it almost black and white, leaving just some color for the red stamp.
2. Another used to bring back some contrast (darken).
3. Now I more or less just used inpainting, blemish removal and healing brush.
4. A high frequency layer in combination with dodge brush (set to highlights) not only adds some more contrast and sharpens the document but also helps removing yellow-ish parts around text and the border which would be a pain to remove with a very small brush
5. That little border chain piece at the bottom had so much detail using the cloning brush didn't look good so I just copied the entire thing (select, copy, paste).
It's also a rather sloppy job a couple black dots are left and I only just corrected the border on the right because the rest is just cloning and painting.
Originally I added the high frequency trying to bring back in some texture of the paper but I didn't like that so I used it in a different way.
The version attached does not show the low frequency layer. The red line at the top border is the inpainting brush's red, it's a very rare bug in APh.