I've been there lots of times...my wife's family is from very near there. If you have more specific questions, let me know.
I'd skip the Montauk trout park and head for the actual river. The fishing pressure is light compared to what you're used to on LMF. I've had good luck parking at the Baptist Camp access and working downstream as far as possible before the water gets too deep to wade across, and then wading back up stream all the way to Tan Vat access, where my wife will pick me up.
You can also float the river and fish as you go.
I've had success on midge larva patterns, eggs, and olive mohair leeches in size 6 or 8. Lots of people like to use crackebacks, but I never have used them
There are lots of browns in the river.
This is a good forum: http://forums.ozarkanglers.com/forum/10-current-river/
If I remember, I can post some pictures when I get home tonight.