Thank you for the answers - much appreciated! A comment, though.
That last part isn't RAW, though. In the book it says that "models are engaged if either is within the engagement range of the other". It doesn't say that you need to end an action within engagement range to become engaged, just that they need to be within range. Then, disengaging doesn't say that you need to start within engagement range, it says that if you wish to leave engagement range with a Walk action, then disengagement happens.
Therefore, RAW, I think that if you walk into, through and out of engagement range in a single AP you would need to declare this intent at the beginning of your activation. But maybe this is against RAI?