[Christopher Brockman]

So, in theory, the issue could be solved by adding enough anchor points to even out the vertices, so long as the first vertices are next to each other?

Also, would I be right in asking if the point with the ring around it is the initial vertex?

[Christopher Brockman]

In the “Save for Web” dialog, make sure your image size on the right is set to the size you need.
Also, check “Clip to Artboard” to crop out any edges that stick off the edge of the artboard.