And this very art is honestly real and true and it is about moving straight and simple, to the nearest target, taking the most direct way. For example, if someone intends to strike or thrust, it goes just like if a string would be attached to the sword and the tip or edge would be pulled to an opening of the adversary – who should be the target for the strike or thrust – resulting in taking the shortest way to the nearest target as possibly. That is why the same true fencing will never employ beautiful and wide parries nor large round moves which are just useful to entertain spectators.
… They[The Leichmeisters] practice wide and beautiful parries and swings when they begin to fence for show, and execute long and far-reaching strikes slowly and clumsily and by doing this they miss and cannot recover again quickly – and thus exposing themselves easily. That is because they don’t have control and measure in their fencing; this really is not part of serious fencing. For school fencing and for practice using this may be useful, but serious fencing moves simply, directly and straight, without any hesitation and pause, just like a string or like everything would be exactly measured and calculated.
He means that an artful fencer, they shall advance the left foot and with hews from the right side directly to the man (and) with threatening cuts so long until that he sees where those can be properly directed and properly reached with his steps.
And if it happened, that the adversary got the Vorschlag (first strike) so he should be well practiced and quick with the Abwenden (turning-off) and as soon as he has turned off the (attacks of) the adversary, he should move quickly as soon as possible, and his point should always aim for the chest as you will hear now. And the point should, as soon as he comes at the adversaries sword, be always within a half Elle (roughly 30 cm) of either chest or face.
Various passages from 3227a, translated by Christian Trosclair
Using these passages, it seems the answer to our question about stepping with the slashes is a resounding yes. Use the slashes to advance and threaten until you reach the distance from where you can land a strike with one more step. Then start your device or cutting pattern.