How should I handle multiple `DmlException` messages when using `AuraHandledException` inside an Apex Controller.

If I do this:

    try {
        upsert value;
    } catch(DmlException e) {
        throw new AuraHandledException(e.getMessage());
    } catch(Exception e) {
        throw new AuraHandledException(e.getMessage());
    }

I get an unfriendly error message, that the users won't like.

> System.DmlException: Update failed. First exception on row 0 with id a0220000005vt34AAA; first error: FIELD_CUSTOM_VALIDATION_EXCEPTION: bla bla bla

If I do this:

    try {
        upsert value;
    } catch(DmlException e) {
        throw e;
    } catch(Exception e) {
        throw new AuraHandledException(e.getMessage());
    }

I get an unfriendly error message which is even worse:

> Unknown Error

If I do this:

    try {
        upsert value;
    } catch(DmlException e) {
        throw new AuraHandledException(e.getDmlMessage(0));
    } catch(Exception e) {
        throw new AuraHandledException(e.getMessage());
    }

I only get 1 of the DML errors and there could be many.

On the client-side I am using this JavaScript code to call controller actions and handle errors:

    callAction: function (cmp, methodName, params, callback) {
        var action = cmp.get(methodName);
        action.setParams(params);
        action.setCallback(this, function (response) {
            var state = response.getState();
            if (cmp.isValid() && state === 'SUCCESS') {
                var result = response.getReturnValue();
                if (callback) callback(result);
            } else if (state === 'ERROR') {
                this.handleErrors(cmp, response.getError());
            }
        });
        $A.getCallback(function () {
            $A.enqueueAction(action);
        })();
    },
    handleErrors: function (cmp, errors) {
        let toastParams = {
            title: 'Error',
            message: 'Unknown error',
            type: 'error'
        };
        if (errors) {
            if (errors[0] && errors[0].message) {
                console.log(errors[0].message);
                toastParams.message = errors[0].message;
            }
        }
        let toastEvent = $A.get('e.force:showToast');
        toastEvent.setParams(toastParams);
        toastEvent.fire();
    },

I cannot find the defacto solution or framework best practice for handling what must be a common scenario. 

Ideally, I'd like a solution which can be used in the Apex controller.

**Questions**

1. Is there a capability built into the Lightning framework to handle multiple `DmlException`'s? 
2. Should the JavaScript handle the `DmlException` rethrow differently?
3. Do I need to write some custom Apex to handle multiple `DmlException`'s?

--

NOTE: this is not a duplicate of [this question](https://salesforce.stackexchange.com/questions/209703/how-to-rethrow-dmlexceptions-as-aurahandledexceptions-right) because he never got a satisfactory answer.