
OK, as one last attempt, I'll take a different tack.

We all seem to be in agreement that there are two explanations for why
one can use the handlebars to lean a moving motorcycle. The question is,
is one of the effect dominant, and which one is it? The idea would be to
design an experiment which would seaprate the two characteristics, and
see which effect produces a similar result to the one with which those of
us who have bikes are familiar.

Let's look at the one that, so far, has sparked no controversy on its
own, gyroscopic precession. To examine this alone, we would have to
get rid of the contact patch effect, by not allowing the contact patches
to transmit any force. The wheels and steering mechanism would have to
remain, and be attached to a vehicle with about the same weight as a bike,
through suspension (so that the wheels transmit forces to the bike the
same way) similar to a bikes. An experiment would be to ride a bike along 
a dry road to get moving and to get the wheels spinning, then change 
surfaces to something that won't transmit forces through the contact 
patches, and try a steering manoeuvre to see if the bike leans. It 
probably would, since some of us know how easy it is to fall down on ice, 
but we wouldn't get a good idea of how well or what it feels like 
because, without the contact patches, we can't turn.  Maybe there's a 
better way. Besides, even ice doesn't get rid of the contact patch
forces altogether, so we'd have to find a really frictionless surface.
You'd have to try it again with the wheels locked to really know if it
was the rotation that did it.

Looking at the contact-patch effect only, however, is fairly simple.
Now we have to find a vehicle that gets the about the same magnitude and
direction of cantact patch forces as a motorcycle, and transmits them
about the same way to the vehicle, but without rotating wheels.
How it gets the contact patch forces is irrelevant, we're just looking
for something that has contact patches that can go straight and not
sideways, and skis or skates would do fine. I don't know of any snow-ski
or skate bikes, but up here we have the Suzuki Wetbike that is arranged
like a motorcycle but has fat water skis where there should be wheels.
I think the propellor is in front of the rear ski, or something like
that, but we could try it at a coast to get rid of most of its effect.
Now I admit that this is second hand info (although I'd love to try
one of these), but the review in the local cycle rag and a guy in
a bike shop that sells them both say that this machine handles very
much like a motorcycle, in that you countersteer it to turn.
So we have contact patches that transmit similar forces to a bike's,
a similar suspension arrangement, and no gyroscopes, but we do have
countersteering.

Conclusion: you don't need gyroscopes to countersteer vehicles that have
motorcycle-like contact patch arrangements. We still don't know what
real effect the gyroscopes have when they're there, but from my observations
of how handlebar angle, force, etc. relate to steering in general, I'm 
willing to bet that they're not the dominant factor in countersteering. 

If you don't like this conclusion, then don't accept it, but my motorcycle's
behaviour is consistent with it. If someone can prove otherwise, go ahead.