Depth takes time to develop in the NHL. The path is rarely draft->AHL->NHL. Prospects spend time in the juniors, or in their national leagues, or in college before hitting the AHL or NHL.
With that in mind, take a look at the current Murray prospects who are currently on the Amerks roster (who are in first place in their division, tied for second in the league):
Borgen
Olofsson
Smith
Cornel
Asplund
Nylander
Johansson (for a few games)
He also drafted Pu and Guhle, who Botterill traded for Skinner and Montour. It doesn't seem that Murray left the Amerks in shambles, it looks like it took the normal amount of time for his prospects to make their way through the system. Botterill has done a better job of adding AHL vets to the Amerks than Murray did, but none of Boterill's draft picks have made their way to the Amerks roster yet.
No doubt that Tampa has done a great job drafting post the 1st round, but they are the exception to the rule. And the Maple Leafs prove this. Mathews, Marner, Nylander, Rielly, Kadri, and Gauthier were all their own 1st round picks. Tavaras, Andersen, Marleau, Ennis, Kapenen, Hyman, Gardniner, Hainsey, and Muzzin were aquisitions.
The Leafs have two home-grown, post-1st round players contributing to the team: Andreas Johnsson (7th round pick) with 36 points and Connor Brown (6th round pick) with 22 points. The Leafs have no home grown players on the team drafted between the 2nd and 5th rounds in the draft.
Murray's approach to building an NHL roster looks alot like Toronto's. Aquire 1st round talent, using your own picks or assets to trade for other team's former 1st rounders, or aquire them in FA.
I don't agree with you on the center prospects. When Murray arrived, the Sabres centerman were Hodgson, Girgensons, and Ott. The team had no center prospects. In two seasons, Murray added Eichel, O'Reilly, and Reinhart (who didn't work out), and drafted Asplund. He was only here only three drafts, so there's not much more he could of done here.
Murray did trade defense for offense, which hurt the defensive depth, but Bogosian's and Kulikov's injuries also had an impact. The McNabb trade was dicey. Murray was trying to build a 'heavy' team up front, like the Kings. Not really the type of game that Blysma was coaching. So yeah, bad trade. And bad choice for coach.
Murray accelerated the salary cap trying to build the top six forwards. O'Reilly and Kane were worth it. Okposo and Moulson, who were a product of a soft FA market, weren't worth their hit against the cap. Again, the strategy wasn't a bad one, but the execution was lacking.
I don't think Murray's issues were with his talent aquisition. Again, if O'Reilly and Kane were still on the current roster, the Sabres (and Amerks) are a playoff team.
Murray's issues were really with his coaching choice, and inability to communicate with the rest of the organization. Botterill might have these same issues. Both GMs and their coaches seem to struggle with setting a winning tone in the locker room.