Any reason not to place stand mounted speakers upside down?

Increase your chair height with a plywood base etc. Leave the Harbeths right way up.

with most crossover slopes you get better phase agreeance between the tweeter and woofer when listening below the tweeter axis.

Try it.

Get about 5-7 feet away from your speakers and sit on the floor. listen to the phase, listen to the mids and upper mids get a lot more snappy and clean. In most cases, that is.

Of course, besides flipping the speaker, you can use IsoAcousutic style pucks to tilt them. :)

I think teo audio mentions the important point.  The pattern of vertical dispersion is generally something like a wide fan, with a 90 degree width and a 10 or 15 degree height.  The fan is aimed slightly downward from the tweeter.  Imagine a cross section of this pattern that looks like a super narrow triangle, the tip of the triangle is the tweeter, and one of the long sides is parallel to the floor and the other long side is angled down by 10 degrees or 15 degrees from level.  So when the speaker is vertically oriented with the tweeter on top, the pattern is just a bit below the tweeter; flip the speaker and the pattern will reverse, it will be ever so slightly upward. So now you need to position yourself slightly above the tweeter.  The worst is when you rotate the speaker and set it on its side.   Now its a a narrow fan offering 10-15 degrees of width and a very wide vertically, splashing HF on the ceiling and floor.   Try it at home, its dramatic how a speaker on its side means that you move just a little bit left or right off axis darn near makes the tweeter almost go away.  This is a good demonstration in your house of HF pattern.  This works with almost every kind of conventional two way or more cone loudspeaker.
Brad

How about sideways?