Can I throw a custom error if a hystrix-protected call times out?

You should be able to get the exception you throw from your fallback by getting the cause of the HystrixRuntimeException

So, to handle your custom exception, you can do this:

try {
    getResourceA();
} catch (HystrixRuntimeException e) {
    if (e.getCause() instanceof MyException) {
        handleException((MyException)e.getCause());
    }
}