I disagree.
First off, to answer your first off paragraph, Type A and Type B are determined by current OVR rating and current OVR ratings only, within specific position groupings. No, this is not ideal, but it is better than your suggestion.
There are too many things that can impact stats to make that a reasonable and reliable alternative for determining Type A or Type B. Home park, for example - you'd have the majority of hitters who play in Coors netting compensation picks; likewise for the majority of pitchers in Safeco.
Piling onto the flawed notion of basing it on stats, basing it on awards may be even worse, since you'd likely run into situations where the clearly most deserving player of, for example, the Cy Young award, doesn't garner votes because he is in a contract year and opposing owners either 1) don't want to see the current owner pick up a first round pick next season; and/or 2) want a chance to sign the reigning best pitcher without having to give up a draft pick for him.