Try CREATE TABLE UNLOGGED with postgres. The diversity of RDBMS and SQL dialects defeats the point of integration testing the persistence layer with SQLite.
even this is less clear - for some dbs it's normal to use a sequence for rowid's (vs some sort of autoincrement) and i don't think sqlite offers all the same behavior there.
You can push complex or db-specific work to slower test groups, but not everything requires it.