You should be able to use the all the gears and cross chaining should never even be an issue. Have him check the gap between the upper pulley and the largest cog (no cross chaining for this calibration), it should be 6mm. Adjust the "B" screw on the RD to the right spec. Most mechanics that are used to Shimano standards set the gap at "just enough" for the chain to clear the largest cog and the upper jockey wheel, which is great if you are using a Shimano RD (I still do this on my Shimano equipped bikes, may have changed). Check also that the jockey wheels and each cog is aligning properly with each gear change.