[SalesForce] Open full width modal from Utility Bar

I implemented a SLDS modal component.

If activated from within a e.g. FlexiPage, all is working well.

When opened within the utility bar using the very same component, the modal is restricted to the lower left area.

Without using an additional (hidden) component on the FlexiPage, how can I open a full width modal from the utility bar?

Edit: You can find all code here, the basic setup of the component used on FlexiPage and UtilityBar is:

<!-- myComp -->
<aura:component>
<c:modal/>
</aura:component>