I like your idea of putting everything inside the bell. I wonder if you could replace the solenoid with just an electric magnet that would pull down the button from inside.
Totally unrelated, I have one project that I keep thinking about starting every time I turn on my monitor in the morning...
I want to connect an RPi Zero to the serial port on my monitor, so that instead of pressing multiple buttons to change the input or color profiles (for day vs night), I could hit a dedicated set of buttons instead.
One physical button might issue multiple commands over serial to the monitor.
I'm thinking of doing this with a Raspberry Pi simply for convenience... I'm sure someone here will suggest doing it with something much smaller, and they'd probably be right.