a few bold humans who I’ve caught plucking from the tree
Let them. You're about to have more plums than you know what to do with, and yes leaving them there will get gross and attract all kinds of critters; you should encourage people to pick your plums, or pick them yourself and give them out. People are suggesting making jam and pies and such but that's a lot of additional work compared to just dumping them on your neighbors.
For picking plums, i recommend using a broomstick or curtain rod to shake each branch, all the plums fall, you pick them up. This should be done a few times a year.