The nature of arbitration--which goes by facts, figures and precedents--makes that sort of argument difficult.
Famously, the NHL's lawyer tried what you're suggesting with Steve Rucchin (who was, at the time, centering Kariya and Selanne) and the arbiter laughed at the argument (which had something to do with a mouse riding an elephant) and gave Rucchin exactly what he asked for, saying his numbers dictate that's what he should make and that nothing else matters.
With Sheary, unfortunately for JR, his numbers are practically indistinguishable from Tyler Johnson's at the same point in his career. He might lose a couple dollars because he's a wing, but I think his arb award's gonna be higher than we want by kind of a lot.
Edit: Now that I think about it, it may have been Brendan Morrison between Bertuzzi and Naslund, not Steve Rucchin between Kariya and Selanne. Either way, the details were the same.
Edit #2: It was Morrison, and the Canucks got smoked in arbitration.
https://www.thescore.com/nhl/news/547156