I have a feeling that Logitech drivers have a feature to change the mouse
orientation, but I only have microsoft mice here. Have you looked for newer
(Logitech) drivers for your mouse's serial number?
I don't recall on the older Logitech Mouseware drivers, but
on the Logitech Setpoint version I'm presently running
(3.1?) there is no such feature. Logitech has v3.3 on
their 'site now, maybe it has more.
There is also an "Uberoptions" tweak for Setpoint that may
(or may not, I've never looked for this in it) provide a way
to do it, or might give hints enough to edit your own XML
files to get that result. Anyway the Uberoptions d/l is on
this page,
http://www.mstarmetro.net/~rlowens/uberOptions/
You could consider a different mouse - there are trackballs (I think they
are called) that would probably suit - their orientation is physical so you
could rotate them to suit. I believe you can also buy trackpads (the flat
'things' on laptops), only I can't find any with a quick web search - I
probably have the name wrong!
Try "touchpad" or "trackpoint" (which only by relation, may
bring up products that have the touchpad in addition to a
trackpoint stick). Most are ridiculously expensive for what
they are, around $50 IIRC. There is one signficantly
cheaper DIY option, to built one (add the surrounding frame
and a PS2 cord) from this base which is complete except for
hacking the pointout for the PS2 pins, and the frame around
the sides and back to protect it (would work without frame
but fragile). I mean a DIY frame design since it had nothing
like that as intended inside the palmrest of some laptop.
http://www.goldmine-elec-products.com/prodinfo.asp?number=G1283
I am sure it's PS2 as I bought one over a year ago and
hooked up a cord to it, but at the moment I don't recall the
pinout, it shouldn't be hard at a glance or with a
multimeter to check since there is only power, ground, clock
and data.