New Yokohama Avid tires on 97 Accord (pull to the left, squirrely handling - endless frustration)

In May, I got a new set of tires of my 97 Accord (170,000 miles).
I decided to go with Yokohama Avids since many people on USENET and
Tire Rack had great things to say about them on 94-97 accord.

After getting them on, I noticed a pull to the left and squirrely
handling. Kind of like the car was tracking every bit of road texture
on the freeway and skidding side to side as if there was constant
crosswind. Definitely not what you would expect on a Honda Accord.
I had a friend drive the car just to verify my hunch and indeed he said
this is an unstable ride.
I wonder if it has anything to do with the fact that these are
directional tires (which by the way look correctly installed by the
arrows on the tires).

To try to correct this, I got a 4-wheel alignment (which it needed) yet
my mechanic still found a pull to the left, that would oddly go away if
the tires were rotated front to rear. But I still had squirrely
handling regardless how the tires were rotated. One rotation
configuration gave me a pull to the left, the other configuration gave
me a wallowy ride on many bumps and dips in the road.

Rotating just the left side caused the pull to appear is one
configuration and dissapear in another. The tire place replaced the
front left tire (with the rotation configuration causing the pull).
Then when that didn't work they took the old tire from the front left
that they replaced and put it on the rear left, and that still didn't
correct the pull.

As you can see this is turning into a complicated and frustrating
story.
The tire place is now saying that they will replace all 4 tires with
another brand.
I am leaning towards Michelin Pilot exaltos.
So I am looking for recommendations and advice on how to avoid another
set that would cause such problems.

Some important info
* My trusted mechanic (repaired only Hondas for 20 years) said my
suspension is in fine shape. He doesnt see anything that could be
causing this
* I got my new Monroe Sensatrak struts in January. I had a set of them
before with no problems and I didn't notice anything odd when they
installed them, with my old tires on.