As someone who's studying statistics, I appreciate your effort to remove your own biases from your analysis by taking a statistical only approach. It's easy to fall into the trap of starting with a conclusion and then find stats to support it (as someone once said, "most people use statistics like a drunk uses a lamppost - more for support than illumination"), and it doesn't seem like you've done that here. When I was in high school and undergrad I used to try to come up algorithms to evaluate players, but I definitely cheated and adjusted the metrics when the results gave me what I thought were wonky results. Ironically, that's what got me interested in statistics, and getting a formal education in statistics is what killed my interest in hockey analytics.
So with that said, I think there are some pretty big flaws in your analysis.
First, sample sizes. It's really difficult to do analysis based on goals as your event because they happen so rarely that you'll have a lot of variance in your data unless you're looking at really long periods of time - like multiple seasons worth - and if you do that in hockey you start to run into problems with conditions changing drastically over the course of the study period. This is why shot attempt based metrics have become so popular - with ten times the events, things stabilize a lot faster. Those metrics still have issues, but that's another topic. This is especially going to be a problem for your playoff analysis. There's virtually no situation where you can draw meaningful conclusions from single digit data points.
Second, context. Players don't operate in a vacuum. You've made some attempt to factor this in by comparing players to their teammates, but you're still leaving a lot out. Things like zone starts, opposition, and on-ice save percentages are huge factors that you should be adjusting for, though this obviously isn't easy to do. Your method is always going to underrate players like Eller and Dillon who get tasked with playing a shutdown role against opponent top lines. Those guys may end up underwater in goal or possession stats, but someone has to go up against the opponent's top line, and if they end up less underwater than any of their teammates would have been had they been tasked with that role, they're providing a net benefit to the team.
Third, there's an underlying flaw in the assumptions about using GF/GA as an individual stat, which is also a flaw with the shot attempt stats. The implicit assumption is that every player on the ice is equally responsible for each goal for or against, which obviously isn't the case. A model is only as good as its underlying assumptions, so this is pretty much a fatal flaw. I don't know of any other sport where it's harder to separate out individual contributions than in hockey. It's what makes statistical analysis of hockey damn near impossible, and why I've pretty much given up on hockey analysis until tracking technology improves enough to give us more granular data.
