The entire arbitration and appeals process is broken.
First, the NHL has complete license to take as long as it wants to schedule appeals. The CBA includes no provisions for due process, so the commissioner can take as long as he/she wants to schedule the appeal hearing, and then as long as he/she wants to issue a ruling after hearing the appeal. It's designed to stretch the appeal so long that the team loses the player regardless of what the final ruling happens to be, in the end. The player may get his money back, but the team still loses the player indefinitely.
As far as the stages go, the first appeal has to go to the commissioner... who has absolutely no reason to ever go against his own office's DoPS. So why have this appeal at all? The reason is clearly to stretch this out. The only thing that this stage of the appeals process does is delay the inevitable appeal to the impartial third-party arbitrator. Which brings us to...
The NHL exclusively selects and hires and fires arbitrators. The NHLPA has no input whatsoever. This is unlike, say, jury selection for a trial. Where's the incentives structure there for arbitrator to rule in favor of the player? Arbitrators make good money for little work, but the strings are there.
This guy in place at present is a dead man walking, as he's already ticked off the league for reducing Watson's suspension. The NHL is going to fire him. Why? Did he fail in his job performance? Well sort of, in the eyes of the NHL office. He had the audacity to rule against them.
Either have a genuine appeals process or don't have one at all. This fig leaf system is just going to piss people off. The NHLPA is going to need to address appeals next go round. Fortunately, it's not going to be long before those talks begin.