Sorry Cody, was that a bit snappy? I apologise - it's just that I've seen wonderful wetland meadows ruined by well-intentioned draining, and wetland meadows are becoming so rare 
. I've a bit more time this morning and I'll try to be more helpful.
If you've a meadow area running down to a beck then you've an ideal place to develop a wetland meadow habitat with lots of specialist wild flowers and herbs. Soft rushes are one of the plants native to a damp meadow.
It's a shame that your meadow was disappointing in it's second year - did you use an ordinary flower-meadow mix? If so that's likely to have been the problem. You need flowers and herbs that grow naturally in damp meadowland, such as those on this list http://www.habitataid.co.uk/acatalog/Wet_Meadow_Seed_Mix.html .
Another of the important things about establish a flowering meadow is how you manage it. The grass will need to be cut late in the summer after the flowers have seeded, and then the grass should be raked up and taken away, so that it doesn't form a thatch and decompose and add its nutrients to the soil because what you're aiming for with a flower meadow is poor soil, not rich improved soil. (The opposite of what most farmers need for grazing.) And the grass should not be cut very short like with a lawn mower - it should be cut so that the grass is left at least 10cm tall - like a meadow, not a lawn. How big is your meadow? If it is big do you know anyone who can cut it with a scythe for you? If it's small you can do it with a pair of hedge shears. Another suggestion if it's big is that you could get someone to lend you a few lambs to graze it in the late summer after the flowers have gone over. Or you could charge them for the grazing to raise funds for more plants 
As for the rushes - is this the Soft Rush? http://en.wikipedia.org/wiki/Juncus_effusus It grew on the farm where I grew up and we used to weave little mats and baskets from it. I love it and it is a native plant of English water meadows, but it does spread - the best way of dealing with it is to dig it out I'm afraid. I'd leave it be down by the beck, but if it starts spreading up the slope further than you want it then dig it out.
Any form of draining, (such as mole draining done by farmers) will be expensive, and you might have to get permission from the Environment Agency to drain into a beck, and on a small scale draining is unlikely to be effective as if you won't be able to lower the water table of the surrounding land, and it will drain into your land.
I hope that's helpful - I'd love to see a picture or two of the area you're working on.
