Some systems use negative Unix time values to represent dates before the epoch (1/1/1970). MySQL does not support this. Does anyone know if SQLite does?
Yes, within limits.
For SQLite versions before 3.16.0 (2017-01-02), the "unixepoch" modifier only works for dates between 0000-01-01 00:00:00 and 5352-11-01 10:52:47 (unix times of -62167219200 through 106751991167).