Any competition of this nature would have to go by type and weight. It wouldn't make sense to pull a 4 pound Hatch against a 10 pound Shamo. Wouldn't really make sense to pull an American against an Asil of equal weights. Doing heats or having some kind of scoring system might work.
Lets say you had an event, everybody bring your birds, first we have a bench show, birds judged on basis of what they are entered as, conformity to an ideal, pretty simple to grasp that one. Lets say that that event scores you ten points for first nine for second, on down to everybody scores one except for the one that may have been disqualified, for instance a white bird that is supposed to be solid black, crooked toes, etc. Whatever the ideal that you use says.
Then you have a pulling competition, I still say it would be easier to let them pull to a mirror and use a scale, then handicap them by weight. There again, first place winner, gets ten and on down to participation points and disqualifications (wouldn't pull) get zero.
Then you have a race. Put the birds own hen that he has been separated from in a cage at the end of a track, say snow fence on both sides three foot apart. Time trials, oriental class will probably run, Bankiva class will probably do some flying. First place gets ten, and so on.
Thirty points will probably take the trophy. Fairly even playing field. You might have an oriental that ran a ten and an American that flew a ten, but it would come down to how they placed in the other events. If you had a tie, maybe an endurance test in a training wheel, or maybe some sort of double enclosure with perches, and the whole thing could be rocked back and forth, and whoever stayed on the perch longest won.
Probably not going to have the draw that some historical events had, but hey, we should probably take what we can get.