One thing I noticed was that my brain doesn't really get 'left' and 'right' - 'same side' and 'other side' make much more sense.

This reminds me of a story from a friend who works in a bike shop. A customer came in to buy some pedals, and asked of the two employees (my friend and her coworker) who were standing nearby, "Do I need to screw one of them in differently when I install them?"

Speaking at the same time, one employee said, "Yes, both of them screw in forwards" and the other said "Yes, the thread on the left pedal is reversed." The customer's eyes glazed over and one of them quickly picked a single way to explain in more detail. The point was that, given three accurate mnemonics for the same thing, you gotta just pick the one that makes sense to you.

I hadn't heard of the Alexander technique before and just looked it up. That seems really interesting. How are you finding it?