I have a manual tranny, but...
Is the tranny pan steel?
If so, you could stick a magnet to the pan to ensure that the broken bit stays put at the bottom of the pan until you can take it apart. Just to be safe...
Also, I have this tool that resembles a telescoping automotive antennae with a small disk magnet on the end. Something like that may be able to retreive the piece through the dipstick hole.
Perhaps you could fashion something similar.
Just some ideas. What a pain!
Best of luck.
1986 300E 5-Speed 240k mi.