Hi,
i also try to figure out how to avoid those "messy" first layer lines. If i print large first layers i got the same problem.
As you can see on your picture, only the large lines look really messy. The outer lines, where the head don´t travel so far until it lays the next line right beside look pretty ok.
Sometimes i`m able to avoid this, by leveling the bed while it prints the first layer like Simon sad. Just restart the Print when you think its OK.