Sasquatch, I've been searching for trout as close to DC as possible since I moved to Northern VA. I'm not the biggest fan of Beaver Creek, it gets too much pressure for my liking (in other words, the fish are too smart for me haha). But there are a few other options that might interest you and aren't quite as far as Beaver. Shoot me a PM if interested.
Another thing I noticed- Some Shenandoah National Park streams are only 2 hrs from Dunkirk, only 15 minutes farther drive than Beaver...
One more thing- TRAFFIC. Try to get to a stream at the wrong time of day and you'll need to add 30-60 minutes to how long you expected the drive to take.
EDIT sorry, thought of something else lol. From what I've read, there is exactly one brook trout stream south/east of I-95, and the population was nearly wiped out by road construction. If that watershed isn't totally closed off to fishing, it's probably a small, super-fragile population you'd be messing with. Point is though that the small streams in the nature preserves you mentioned are almost certainly not worth the effort. Just too low gradient in that area and what streams do have some gradient also have easily eroded soils.