Aaron,
You asked where do the attendant bees come from when the banked queens are
above
a double screen (I know it is a Snelgrove board, but who else does?).

There are two different ways and I have done both. You MUST have an outside
entrance to the hive body where the banked queens are located, either an
entrance made in the double screen board (like Brushy Mountain's) or an
Imirie Shim, or an inner board front
entrance (which I prefer).  I mentioned two different ways: 1) put a frame of
open brood or capped brood and adhering bees in the hive body with the banked
queens; but you run the risk of emergency cells if you use a frame of eggs or
young larvae.  2) have frames of fresh nectar in the body with the banked
queens.  The forager age bees
will forage from that hive body and attend to the banked queens also.

My choice of the two is to use a frame with both open brood and capped brood
present
and this can provide nest bees (non-foragers less than 19 days old) for up to
about 5 weeks.

I hope I have answered your question.

George Imirie