The difficulties of being weirder than English

Lately I've been rather cross about having English for a first language.
I want to invent something exotic and unique, but two things have made
me realize that English is already exotic, and I feel cheated :)

The first item: somebody here posted an interesting link a few weeks
ago to Talmy's typology of verbs of motion
(http://elies.rediris.es/elies11/cap2.htm, if anyone's interested).
I had never taken apart verbs of motion that way, and it was very strange
to realize that English, in lexicalizing *manner* of motion rather
than *path* (though we have also inherited path motion verbs ("enter",
"exit") from Romance languages), would actually be quite fascinating and
exotic - if only it weren't so familiar!

Item the second, I was reading Language Typology and Syntactic Description:
Volume 3, Grammatical Categories and the Lexicon, the article on Tense,
Aspect and Mode.  They mentioned that some languages in some situations
mark *both* absolute and relative tense, and (perhaps not being quite
awake yet) I thought, wow, that sounds cool and interesting, maybe this
will look like the Caucasian verbs that agree with 4 or 5 nouns in the
sentence.  But when I got to that section, the example language was -
guess what - English.  Of course.  We have verb structures like "will
have done".  I should have known...

I guess there's nothing for it but to pursue my ideas for languages
spoken by aliens with a different psychology :)  So, anybody have any
ideas what kind of social organization would lead to a language that
doesn't distinguish between singular and dual, but does distinguish
between singular/dual and plural? :)  Or, perhaps, agrees with odd vs.
even numbers? :)

Amanda
Actually, trying to work on a relatively normal noun-incorporating
polysynthetic language (if by "work on" one means "agonize over in very
abstract terms, then go off to do more research")

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