It's a bad example because you are focusing only on one part of the equation and that is Hand, the separation of the compete level and organization of an NHL team in the 30's is a huge cry of what it was circa 1903-06.
Comparing the CAHL/ECAHA to the NHL of the 30's is at least a relevant starting point and fair game for discussion. Though rather than this you chose the British Super League of the 80's/90's, and provided no evidence beyond your own musings that the BSL was of comparable quality to McGee's leagues.
It's obvious Hand doesn't belong in the discussion, what you are missing is that while the separation for Hand is largely a space thing, ie he choose to play in a weaker league, for Frank it's a time thing (and not really relevant if there was no other choice or not) and the state of hockey in 03-06 is closer to the Hand situation than it is to anything we see in the recent past.
If it is obvious that Hand doesn't belong in the discussion, why was he introduced? You readily admit Hand chose to play in a weaker league, while in McGee's case you make no such assertion; rather, McGee is, in a vague manner, criticized for "the state of hockey". The idea that McGee's impressive play in the highest regarded league that existed in Canada in the early 1900's, which produced several Hall of Famers, is comparable to Hand's impressive play in a league not known to produce any players of any historical note whatsoever is again surmised without any reasoning besides what year AD the calendar displayed.
McGee simply doesn't stand up in a direct comparison to Stamkos his 3 years simply isn't anywhere near the level that Stamkos has played at, if there is any serious consideration for context.
McGee was one of the top goal scorers in the game for four seasons, identical to Stamkos. Both players were considered amongst the very best in the game, with perhaps one or two others seen as superior. Russell Bowie and Hod Stuart, Sidney Crosby and Evgeni Malkin.
Stamkos' yearly placements in the goal scoring race are 1st, 1st, 2nd, 2nd. McGee's are 1st, 2nd, 2nd, 5th. McGee's 1st came in the FAHL in the year the Senators split from the CAHL, so it quite possibly would have only been a 2nd (to Bowie) in a consolidated league. The 5th is in a half season after Ottawa withdrew, and projects to 2nd (again to Bowie) had McGee been allowed to complete the schedule. Edge goes to Stamkos in raw finishes. Assists were not recorded in McGee's era. Stamkos is not a prolific playmaker. Difficult to determine who would have the advantage without further study.
Playoffs, McGee was his team's most prolific scorer in a Stanley Cup victory over Russell Bowie's Victorias in 1903. Ottawa accepted a challenge from Rat Portage afterwards, and McGee was again a significant factor in Ottawa's victory over a team with three future HOFers. Ottawa defended the Cup the next December against Winnipeg, McGee scoring a goal in a 2-0 victory described as "the most brilliant game ever played in Ottawa".
Ottawa fell behind in a 1905 Cup series against Rat Portage, losing the opener 9-3 with McGee out injured. He returned for the next two games, helping the Silver Seven comeback to win the series with a hat trick in the decisive 5-4 victory in the third game.
Ottawa hammered several over-matched challengers as well during this era. McGee's scoring exploits against Dawson City among others are notable, but contribute little to his playoff legacy as it would pertain to this project.
Stamkos performed well in his lone NHL playoff campaign, 13 points in 18 games. Noteworthy that he was knocked out of Tampa Bay's Game 7 against Boston due to a puck to the face, but returned to the ice as soon as he could be sewn back together. Nonetheless, playoff accomplishments are decidedly in McGee's favour for the moment.
As you can see, these two players are extremely close in a direct comparison, preference for one over the other likely resting on whether one feels McGee's Stanley Cup exploits overcome Stamkos' regular season proficiency. People may choose to dismiss McGee's case on the basis of his year of birth if they wish, but it is difficult to do so without dismissing his entire era as a whole, which would seemingly go against the project guidelines.