Coach:
In the basic LL rules, as long as the batter-runner is gaining ground (does not matter how he modulates his speed), he is legal to attempt to gain second base regardless of whether or not the battery are set.
If he reaches first base, takes a turn, and then stops, as long as the pitcher is on the rubber with the ball and the catcher is in a position to catch (does NOT have to be crouching), then the runner IS in violation of 7.13. If the pitcher attempts a play or steps off, 7.13 is moot.
What you have described is legal.
Mike CVUA