Leveling and trueing the structure will take a little time and patience. There will probably also be head scratching.
Again, there are several ways to do this. My technique might not be the absolute easiest, but it turned out pretty well.
Remember those "cheater" beams we made out of the 2x6 boards? Get those out and set them on top of each post. Screw each side into the top of the posts with two deck screws. The position of the cheater beams should be consistent across the center on all posts. In my case, the ends of the cheater beams (points) just stuck over the outside of the posts by about 1/2 inch.
Now take the 2x2 braces and screw one to the top of each post. Hammer in the anchors next to where the brace touches the ground but do not attach them yet. You have some extra braces to use if you need to anchor a couple of posts from two directions.
Time to measure everything again. Make sure that the cheater beams have exactly the same dimensions that you recorded for the beams you cut and laid out on the ground. They should be completely true but do not yet need to be perfectly level.
Once the hexagon is true, screw the bases of the braces into the anchors. You might need to anchor one brace, check dimensions, then anchor the next. The goal here is to make the hexagon perfectly symmetrical a tthe top. The poles themselves can be a little crooked.
Ok, now that the top of your structure is symmetrical, you can use the post level or box beam level to ensure that each post is perfectly straight. You may need a little leverage to move the bottom of a post an inch or two. Use a shovel or a rock-breaking rod. Do not forget to check the beam measurements each time you move a post to make sure it is all still true.
Once the posts are straight, you can level. I did this by setting my 8 foot box-beam level on top of each of the cheater beams. For low posts, pour in a little paver base and lift up the post to allow the paver base to flow under it. You may need to disconnect the brace so you can lift the post.
Keep leveling all the way around the structure until all of the cheater beams are level. I ended up with one that was about an inch high and decided not to pull the beam out to dig more. Only I notice.
Once you have the post-tops level, measure all of the beam dimensions again. Chance are good that something moved slightly. Adjust and reattach the braces as needed.
Once everything is true and level, pour a little gravel or paver base into each hole to ensure that there is drainage at the bottom of each post and that the post isn't going to move as you pour concrete.
Mix and pour the concrete one bag at a time. Pour it in evenly, then jam the concrete in around the post with the iron re-bar you used as the center marker. The concrete should stop at or just a little below grade. Angle the top edge of the concrete so it will channel water away from the post. Let it dry overnight.