And don't worry so much about cross chaining. On most modern drivetrains, you can crosschain a double, all the way across without any problem, other than a bit more noise, and wear.

Even if you're fastiduous about minimizing friction, and wear, you certainly can use 6 of the 8 cogs, with each chainring (i.e the 6 biggest with the small front ring, and the 6 smallest with the large front chainring.)