iPurpl3x indeed there's no event or extender for that as I can see. And I can't think of any extension that has its own ExceptionHandler.
Here's something you might be able to do (I have not tested)
// Resolve the ErrorHandler singleton
$handler = app(Tobscure\JsonApi\ErrorHandler::class);
// Add yours
$handler->registerHandler(new YourExceptionHandler);
The trick is where to run that code. It needs to run after the ApiServiceProvider registers, so there should be many option. The most logical might be to register your own service provider, and run the above code in its boot method.
Related but not actually the same, https://github.com/flagrow/html-errors is an extension that registers a middleware to catch specific errors and return an alternate response. But it's for the front-end, not the API.