Hi Blubelle
Yes, my immediate reaction when I saw Gilchrist was Scotland at some stage.
Some of my Irish relatives came in through Scotland. I've got them on odd English censuses, and they must have passed very close to us in Cumbria, but I'm having a job to pin them down, even though I'm on the spot. I'll keep an eye open for yours as well. Bates and Gilchrist aren't so bad, but Thompson's quite a common name.
Have you tried Scotland's people? You have to pay for credits, but you can narrow things down if you keep changing your search criteria, even down to the exact parish.
Good luck!
Emms