If I understand…
You could download and install this addon for Connections:
Click the green button to download the zip file and then install as you would any plugin in WP.
This adds a new settings option on the Connections : Settings admin page under the Advanced tab.
You could choose to split out your services category. And then under the Display tab in the Single Entry Content Block section enable the Services block. And then use the Template Customizer and disable the category display.
Doing this will now only list the categories under the Services category.
Hope this helps!