I agree completely. However the NHL did try to get some modest and realistic exemptions into HRR, and the PA flipped. Trying to actually determine HRR by the median would never fly.
I don't think you need to "determine" HRR by median. You simply guarantee the players a percentage of the median HRR (times 30). But make no changes to how HRR is arrived at.
It could be a higher percentage than the 57% of total HRR now. You could give the players 61% of median HRR times 30; about the same dollars as 57% of total HRR.
You'd simply be reducing the floor/cap to be more inclusive of all the teams. Any increase in revenue sharing (total dollars) would be a very small percentage increase, but there'd be more teams over the median than are over the average; so there's more RS dollars (provided by teams 11-15 in revenue).
There's fewer teams below the median, so those dollars bring up everyone below the median.