It doesn’t really smooth out much when I do what you suggest; it just slows down faster.
Even with a dead straight sleeper throw, it visibly oscillates with high frequency “wobble”. I mean, I get a certain amount of this with all my plastic yoyos, but with the others I can usually achieve a throw straight enough and strong enough that I can’t really see or feel the wobbling, just not with my Wedge.
Hmm… Can you share a video?
The weight of the yo-yo is not what carries it down the string in my opinion - it should be 90% your throw. Sounds like if you can really focus on snapping your wrist better as the yo-yo comes off the hand that will help better propel it down - but I’m definitely guessing a bit without seeing a visual.
This was with WEDGE Specifically?
I’m not sure how to attach a video here.
I guess the usual procedure is to upload a video to YouTube and link to it in a forum post?
Yeah - Either post a link to a video uploaded to YouTube, Instagram Vimeo, etc. The forum software is great for pictures but video takes up a lot of bandwidth so best to use a website built for it. 
