How to keep a buried sump pump pipe from freezing without digging it deeper in the ground

About the only way you're going to stop your pipes from freezing is to install them below the frost line. Iguess you could try digging the drain up , encasing it in PVC and Armoflexing(see image) the drain but I surely wouldn't guarantee it wouldn't freeze.
Sorry I couldn't be more helpful but I'm a Florida plumber and we don't have a frost line in my area.

Where do you live and what is your frost line? If the pipe drains to open air it will probably never freeze solid.