Can I switch between saved stream crops with a keyboard shortcut?

Yes. Save each crop in a separate stream configuration, then use BetterDisplay's Toggle Screen Stream action in macOS Shortcuts to start or stop the configuration you want.

Open the source display's Stream Display or Stream Virtual Screen menu. Use Add Stream Configuration in the original entry to create another numbered configuration. Set up its target, crop and transforms independently. These settings are saved per source and configuration. Stopping the output does not erase them.

In Shortcuts, add Toggle Screen Stream and specify the source display, target display, stream configuration number and On state. Assign a keyboard combination to the Shortcut. Streaming requires Pro and the applicable capture permission. Keep BetterDisplay running and both the source and target displays connected.

To replace one active crop with another, put an explicit Off action for the old configuration before the On action for the desired one. This gives the same result each time you run the Shortcut. Select the target display in the On action, because stopping a stream can clear its saved target. If several configurations may be active, add an Off action for each one you want to replace.

CLI and HTTP integration can address the same numbered configuration using specifier, for example specifier=2 for configuration 2. Create the configuration first. Then include its number in the command that starts or stops the stream. See macOS Shortcuts, Streaming and stream filter commands for further setup and filter adjustments.