Your top 4 are solid for now, but after that it is a complete scramble.
You hit it on the head with Washington and the health issues which loom large, but they are likely in the running for the 5-8 spots.
Cleveland has LeBron and
I literally hate the rest of their team, has beens, old guys and never were's mostly. The few useful guys are pretty flawed. They have a ton of expiring contracts so I expect them to be busy at the trade deadline. If LeBron even gets a partial season injury, say 20 games, they could be hard pressed to make the playoffs.
Miami still looks like a bad team to me. No PG, no C, Wade is always a good candidate for the IR at some point and Beasley and Marion look like they might get in each other's way. I don't think Riley would mind one more trip to lottery land before they go after Boozer next summer. Expect their big turn around to more likely happen next year.
Charlotte will make a trade a week with LB and MJ in charge, but they will improve some, who knows how much.
Milwaukee, meh? They still look a mess.
Even if they just re-sign their own RFA's, both Atlanta and Philly will improve based on internal maturing of their younger players. Not as exciting of a way to improve as FA, but it should happen for both teams. How much improvement is to be determined. Things would definitely tilt in the Sixers' favor if Smith signs here, and if not we still have cap space to make other moves this summer or at the deadline. Plus we had a first round pick this year and they did not.
Chicago has to make some more moves, specifically for a post scorer, but could be this year's turn around team from last year's lottery.