Absolutely,wider moves are great
to fell your picking and every note you pick.
At faster tempo you cannot do it that wide
because there is no enough time,
but that won't be the problem cause
you "get the idea" when practicing slowly,
just as you said.

Now few words about the take you provided,
Timing is 100% ok, picking hand does it very smoothly
so I really have no suggestion on that matter.
The only thing I noticed is the moment when you played
Em7 chord (without 5th), it sounds a bit muddy
but it's just related to the way you hit the strings.
Try it with more attack and also angle the pick a bit,
to get more brighter tone,you can even add more
treble and cut some middle in your tone.
Those grips/chords might sound not so great when played on
distortion but all you have to do it to apply more
power and attack when you play them.
Also you can apply the same to the whole section/lesson,
it will sound even more solid and steady.
All in all it's very well done,good progress.