>  has anyone ever tested the hypothesis that swarm vs stay is lines up with the genetic-relatedness to the leaving (or staying?) queen?

* Yes. I was going to add to the previous post, if anyone cared. Juliana Rangel looked at this and wrote her PhD on it:

[We] looked at the question of whether honey bee workers make a decision of whether to
stay in the old nest, or leave with the swarm, based on their genetic relatedness to the
queen(s) that inherit the nest during colony fissioning. Our findings showed that there
is no intracolonial nepotism during swarming, despite the theoretical prediction that
workers should benefit from preferentially staying in the old nest based on their
genetic relatedness to the daughter queen(s).

SWARMING IN HONEY BEES: HOW IS A SWARM’S DEPARTURE TRIGGERED AND WHAT DETERMINES WHICH BEES LEAVE?
Juliana Rangel Posada, Ph.D. Cornell University 2010

* As to the age of the bees, Butler marked bees of definite age and documented which bees went with the swarm:

> there is no doubt at all that a swarm is largely composed not of the older bees, as has previously been assumed, but of the younger and middle-aged bees. This is, in my opinion, what one might expect since a swarm usually emerges at a time in the day when the majority of the older bees are already out foraging (as shown by scale-hives) and are therefore not available for swarming, the complement of the hive mainly consisting at this time, as shown by Rosch and others, of younger bees.

THE AGES OF THE BEES IN A SWARM. By C. G. BUTLER, Rothamsted Experimental Station. Bee World

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