Do the newer songs simply stop being uploaded? Does the iTunes Match splash screen display a big nasty "sorry you're over the limit" screen? Is there something I can do to get it to only work with a specific set of songs (shy of deleting them from my library)?
The 25,000 songs is for the songs that you've added to itunes match and are not purchased from the itunes store. If you exceed that limit you will just be able to able to add to your itunes match library, songs that are purchased from itunes.
You can delete specific songs from your icloud library (right click>delete from icloud), there is no need to delete them from your local library too.
And yes, it just displays a popup mentioning that you've reached the limit.
This is all documented at https://support.apple.com/en-us/HT204146