I wonder how one manages to get dealt the appropriate mix of odd and even cards to play mike' s suggested method

The probability of not having the 'right' cards for this signalling method is the reason advanced by Michael Rosenberg in arguing that odd/even methods carry with them an almost unavoidable risk of giving U.I. on defence.
I have played odd/even with a very good partner, who is extremely ethical at the table, yet there have been times when I was morally certain (and correctly, it turned out) that his signal was not accurate, in the sense that he had no accurate card to play. I stress this was not due to any lack of ethics on his part, and the situations arose infrequently, but sometimes the need to analyze which misleading card to play requires a small tempo break.
As to the posted question, I do not believe that it is possible, in any normal method including 'obvious switch', which I play, to combine count and attitude at trick one. One must choose one or the other.
As most do, I change my methods at high levels, due to the increased likelihoods of either needing to know whether the second trick will cash or whether partner has the K.
Thus I am far more likely to lead an unsupported A against a high level contract than against a pedestrian 4
♠ or such. So I need attitude when I lead an Ace. This makes me lead K from AK or KQ, relying on partner to give me count so that I can cash the A when necessary (if I have KQ, either declarer wins the A at trick one or we can usually work it out)
It is possible (I think Vinje wrote on this topic) to change your methods depending on how many cards hit in dummy, but I don't think he was discussing the posted problem.
BTW, the switch in time book focuses on attitude, relative to another suit, the identity of which (the obvious switch suit) is determined by the defenders according to a set of rules, relating to the auction and the appearance of dummy. I do not think it will help resolve the posted issue.
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari