"In another post, I read that someone took out the Primo thermometer, and put the grill temp probe through that hole. In another post, someone reported that they did that and did not get good temperature readings."
The BBQ/grill temp probe comes with a clip to hook it to the grate wherever you want to measure temperature. You can't just poke it thru a hole and let it hang which is probably what they did. How you route the wire does not effect temperature readings, it's where and how the probe is placed.
Oklahoma Joe Offset
Modified SNPP offset (retired)
Weber 22.5 OTG
Super-Fast Thunder Blue Thermapen