A few things come to mind:
1- Deal with any turf first. Lumps & roots will give you fits when dragging with the BB. Skim sod to be used elsewhere, or perhaps relaid there.
2- Work down from the high side with the teeth fully down & the blade level above surface to loosen-up the deeper soil. Stagger or cross paths as you go. A subsoiler will do the same thing with a few more passes. Once softened, things will level pretty easily and you might even take the teeth out to grade.
3- Set the stop or note where your position control lever is to get the smoothing you'll want to finish. In the right position, you may be able to go back & forth when set at the right height & 'tilt'. Hand raking last on such a small area before seeding would be indicated. You tires will leave a few grooves if you don't use them to compact the entire area. (a BB used
without position control would be as handy as a sea anchor, glad you have it)
4- Use top link adjustment to tweak depth of cut or the amount shaved when dragging with the box 'floating'. There will be a sweet spot that shouldn't be hard to find.
5- Use the FEL for where the BB won't reach. It'll will scrape going forward nearly as well as the BB, and back-dragging may be the easier way to get the final level. Depends somewhat on soil texture or amount of moisture, etc.
If you haven't done much of this before, IMO you'll be darn good at it even after doing an area this small. You may get the urge to make parking lots to further display what you can do after the experience.