I disagree that this is a draft the Hawks can not move up in. I think last years was deeper and therefore harder to move and the first time no picks were getting trade on draft day. flat cap and weak free agency class also played a factor along with the stronger draft class.
If the Hawks want #10 from NJ, they simply offer #18, #34, & #50 and I can not see NJ saying no as that is an overpay to the equivalent of a 2nd in the 40's on fair value. If they do, you offer #67. If they say no again, you offer Dallas '25 2nd. There is a point that the value becomes to compelling to say no and the Hawks have the chips to not only do it, but I would argue should do it. You can't keep taking 6, 7, 8 top 100 picks draft after draft after draft and have that work. There are only so many roster spots in the AHL and NHL and at some point you will start losing lesser prospects who will wait out free agency to go to organizations with easier (or one at all) paths. You can keep using all these 2nds and 3rds to pick players you likely end up losing some for nothing in 2 or 3 years because there are no roster spots, or use the draft picks to "overpay" to move up and consolidate into better prospects.
Another approach to subsequently moving up may be acquiring a 3rd 1st round pick first. There are a number of teams with very few picks this &/or next season that should be open to trading down for more kicks at the can. #19 Vegas has 1 pick & LA has 2 in the first 5 rounds. Colorado and Toronto only have this years 1st rounder in the first 3 rounds of the next TWO drafts. Every one of those teams should have a interest in trading back to acquire multiple 2nd/3rds over this and next draft.