Of course most people who have complex queries are probably not using sqlite and so may not care about testing the database.

SET SESSION synchronous_commit TO OFF;

(Update: I just looked in our test code, you can also replace the CREATE TABLE commands with "CREATE UNLOGGED TABLE" to disable write-ahead logging.)

There are possibly other tricks?

I slightly disagree with the tech debt comment, though. If you get a huge speed up, it may be worth paying for the occasional bug, depending on the circumstances. Or you could do both, and only run the test on Postgres occasionally.