If you want to keep the desk, you could always get a larger piece of wood (try to stain it to match), throw some felt padding in between the top of your desk and lay the new piece of wood on top
It looks like there's a lip around the edges, so if you make it wider but keep the depth the same, you could throw some of these along the back to keep it in position a bit better - https://www.amazon.com/LEADRISE-Universal-C-Clamp-Desktop-Worktables/dp/B08JYDWMR4/ref=asc_df_B08JYDWMR4/
Or if you want to go a bit larger, you could throw some stop blocks on the underside of the large desk on the sides and the back. It won't move left or right from the blocks, forward would be stopped by the blocks. Backwards would have a little gap if you weren't right up against the wall, but at least it would keep the drawer accessible.
I wouldn't go screwing or nailing the top to the desk, definitely wouldn't want to ruin something that sentimental, but might be able to give you a bit more usability
I have a metal I-beam running across my basement that I attached C-Clamps too. On the C-Clamps I through on some carabiners, and attached lashing straps to those. It's a nice little solution that eliminated the need for any kind of semi-permanent fixtures.
It provides a lot of versatility as I can adjust the length to fit my needs quickly.