The suspension on the S and E models has been the same since 2002. The suspension on DRZs is actually good for trails. The biggest problem with the S is the weight. Not only is it just plain heavy, ot is very top heavy.

If u look at kawi...the kdx would be good(if u can get it plated)
As far as dual sports, Don't bother w/the KLR 650...way to big and heavy!
The KLR 250 is just a TURD(bought a new one, sold it 2 months later)
The klx 250 and 300 would probably be your best bet for a dual sport in the woods(if you go with a green bike) with a few mods...great for trail riding, but not sure about hopping on one in a race though.
haven't ridden any others, so i can't really comment on them.

when it comes to buying a bike just be patient and wait for the right one.  I bought my plated 2003 kdx 220 for $1700 with a ton of aftermarket stuff and i bought my plated 2004 crf 250x for $1750.  Its a little more than what you budgeted for but the deals are out there to be had you just need to be patient.  I just raced my first enduro a few weeks ago with the kdx and it was great.  It was a Dual sport run at a total of 70 miles.  I entered in the c vet class and went out and had fun.  my goal was to finish the race.  don't listen to  some of these nitwits that tell you every bike is junk except for the brand they're riding.  i've seen plenty of experienced old timers pick people off one at a time on their 15 year old bike bikes.  i will agree with some of the people about trailering your bike to the event.  hare scrambles and enduro's can be pretty tough on your bike and it would suck to have a breakdown with no ride home .
Hornet