I'm looking for the magical solution which will allow me to wire my recessed
lights across joists without having to tear up the drywall in the process
(for drilling the holes in the joists).  Please give me the instructions for
this magical solution so I can install the lighting that my wife is asking
for...

(its the 1st floor of a 2 floor house, no topside access).

Well, you have to make holes for the recessed lights anyway, right?
If you're putting the cans every 3rd bay, you should be able
to drill holes through the joists using one of those 48"
flexible-shaft bits from where the cans go.  

Depending on how far apart you want the cans, you may be able to pull
it off.  Search for "flexible drill bit".  Several manufacturers make
them.  You would cut a hole for the first can, then use this through
the hole to drill through the joists to get to the next hole.  You can
get through 2 or 3 pretty easily, and if you work from both sides you
can manage spacings of 4-6  joists with some fair amount of fussing to
feed the wires.

Use remodeling cans, which let you stuff all the works through the
round hole you make for the housing.  You wire them while they are
hanging out, then stuff everything up through the hole and snap in the
trim.

Just be careful you don't drill through something important, like
another wire, pipe or heating duct.  Avoiding (and locating) that kind
of stuff is often the hardest part of the job.

HTH,

Paul

I can't imagine a safe way to do it.

Drill through a wire or a duct and your probems have increased - if
you're still alive.

Do you have crown moulding in the room? If so you could remove it and
a little drywall to access between each joist.