Hello,
(no problem, your topic is where it should be)
I am afraid you have only 2 options at this point: in the contact information, select the 'link a' in the 'fields' section or in the 'links' section. In the 'fields' section you can add a label to your link (Read more) but the link will show following your label. In the 'links' section, you can only have an icon, which you can override with CSS (the web icon is the icon by default). You could also use CSS (the :before selector) to add your own label to it.
But in your case, the 'ideal' solution would be to actually have the 'link to contact' field go to the 'link a' instead of the contact itself, if I understand your configuration correctly. I will see if I can add this option to the next update of the component.

Ok, I saw your page, looks really nice. With the way the component is built, it is not easy task to make the label the link. I actually think your best bet right now (until I add the feature 'allow contact to link to links a, b or c' to the component) would be to override the contact page. It is actually simple to do. What you want to achieve could also be done just with simple CSS (just use display:none on all the elements of the contact page you don't want!)