Not overlooking the possibility that someone else could be correct (in this case MikeSS) I researched the issue a bit. From the AoA website specís for the TTS which has a 6-speed S-Tronic it appears gears 1-4 use the lower (numerically higher) final drive ratio and the top two gears (5 & 6) use the higher (numerically lower) final drive. Applying this to the S3 I came up with the following table.
This provides the sort of progressive steps in overall gear ratio the OP was looking for. This is further confirmed on pages 32-35 of the Self-Study Program for the 6-speed S tronic (link provided in a previous post). These pages show gear speeds 1-4 using output shaft 1, while gear speeds 5 & 6 use output shaft 2.