Trying to look at this from a harshly objective position, anything more than $8M is an overpayment. Carlson had a 55 and 68 point season prior to signing. He also had 20 points in the Cup run in 24 games. Hamilton has yet to break 50 points. Admittedly, he was on pace for 69-70 this season, but the 20 games before the injury he had 12 points, which is back to his career production. In last year's playoffs he had 7 in 15.
Paying more than $8M is betting that Hamilton will produce for 7-8 years like he produced for only 3 months during his career. Given this front office's style, I don't see them making that bet. Also, at some point having Hamilton for, say, $8.5M for 7 years will mean tough decisions on the other players that have been mentioned.
Of course, if a deal is delayed and Hamilton puts up 70 points in 20-21, then $8M is a good deal.