Have you thought of haveing the tranny looked at?
It may just need a cable adjustment or something.
Have you changed the fluid?

I'd go to the Honda dealer and non-dealer tranny shop.
Get quotes from at least 2 places for the problem. Going to more then one shop will help limit scamming. Be up front about the estimate thing too.

No matter how you look at it, even if you need a new tranny, it's cheaper then a new car.