Essentially, you can't compress compressed data. There are tricks that can help with some data, but probably not with the data you present. Something like what you suggest can work well for digitally sampled analog data where most of the information is in the low bits so compressing the high bits of the samples separately can be advantageous. Doing that where all the high bits are the same for the entire data set only bulks out the final result.
Optimising for fewest key strokes only makes sense transmitting to Pluto or beyond