How to stop building synthetic species in a full world

After you have been the overlord of a vassal for a certain amount of time, you can initiate the "Integrate Subject" process from the diplomacy screen.

Communicate with the vassal and select the option; it should be the bottom most option available. If you haven't been the overlord for enough time, the option will be disabled, but still visible.

When you start it, you will be shown the amount of influence required to integrate. This cost is split across a number of months, with 3 influence spent per month. This total cost varies based on the size of the vassal, with larger vassals requiring a larger amount of influence (and hence time) to be spent.

Plan A: As they come within your borders.

Give your construction ships orders from the Galaxy View Instead of the System View unless you are:

• Ordering up a military station.
• You are mineral poor.

When a new system enters my borders and I've got a free construction ship, I'll select the ship, and right click on the new system to build any applicable stations. For those few times a primitive species is in the system, you'll see "build observation post" in the menu between "build research stations" and "build frontier station". This is the easiest time to build observation posts.

If you do use System view to build your utility stations one at a time, the civilization's icon to the left of their world name should also be a pretty big flag that it is a site for an "alternative research station"

Plan B: Go back after you've already built up the system.

This one is a little more fiddly. Open up the "Contacts" report and uncheck the 3 boxes at the top which don't represent the (grey) primitive species. At this stage, you can iterate through the list and click on the camera-like icon to focus your view on their home system. If they are within your borders, send a construction ship. Do this a couple times and you'll start to see the virtue of Plan A.