I always remove the cores.
- Mount the tire
- Slather bead with Schwalbe mounting fluid (soapy sponge works too)
- Use injector or just the small white bottle to put the Stans/fluid in the tire
- Use a blowgun or airshot pump to seat the tire
- Holding finger over valve stem, quickly replace core
- Air back up with floor pump
I don't remember ever having an issue with the tire unseating.