You can join a faction to lower crown authority (if your liege is the emperor, anyway, which he probably admittedly isn't), although you're right in that expansion can be slow if you have bad luck with claims.
For the HRE in particular, the major reason they tend to hit Medium CA quickly is that they are an elective monarchy, which means their vassals get +30 relations with them. Getting the Empire to Primo or, better, Gavelkind succession early on is a good way to both halt the CA creep and implode the empire. Trick is, of course, getting that duchy in time to do all this, which is sort of paramount to succeeding as a non-indy count.
Bear in mind that you can still plot to fabricate a claim on and to acquire a duchy even at Medium, High or Absolute CA. Wars against your liege are, IIRC, still fine regardless of the level of crown authority you're working under.