I think the most important thing is to start looking for a job.
From the sounds of it the LANTRA Professional Tree Inspector course will help you the most, it's a short course, not expensive and packs a lot of punch on the c.v (it was the first course I was put through when I joined a consultancy), can't see much point of a level 4 if you have level 3 (plus experience) and a level 6 will be better tackled / more relevant once you have experience as a tree officer or consultant.
Local government Tree Officer Jobs might need minimum requirements (such as level 4), but it'll just depend on how they word the job spec. (essential vs desirable), but this will be apparent in the job advertisement.
Consultants might be different; if not part of a larger firm they won't need to go through all the HR red tape. If you want to try consultancy over a tree officer job write up your c.v and send it off to some consultants in your area, whether they are posting job adverts or not.
Good luck.
