May I say how amazing your graphics are?
have a look. I fixed the horizontal problem by shaving 1 pixel off EACH side of the Player.boundingBox
I also moved the image point by one pixel vertically, seems to have solved some of the vertical jiggling.
I suspect you need to play with odd and even numbers in your dimensions and image point positions.
Also, it might help to pin your accessories to the player sprite, instead of setting their position. But even then, you need to find what numbers play well with Construct's engine. Remember, if you force Construct to divide a pixel in half, it's going to have trouble deciding which half, which I suspect is the cause of the jitter.
A 1x1 pixel player sprite might work, but then you need a new "player" sprite for collisions and the like.
Let me know if this helps.