Another way that makes sure your line isn't on the surface is to deliberately cast over a low twig. You can't do it over every branch, it has to be one your line can fall from easilly enough when a fish takes.
Using wind-drift to help you get around the far side of a tree can be very useful once the carp know you are there and they won't come out from the cover.
I've had my best results this year with 10lb, Berkeley Vanish fluorocarbon line as a leader or long hooklength. In fact it wouldn't sink without the Korum Quickstop on, which surprised me as a 4lb. fluoro hooklength and a wet 'dry-fly' sure sinks quick enough!
I used too stiff a rod and got some breaks, so I went to 15lb ESP fluoro and it was useless on the top. It sank so quickly it actually pulled the bead and the bait together as it sank in a great loop!
It seems the 10lb. fluoro from Berkeley was just right, with a little 'help' it just sank under the surface, but didn't sink any further. I just had to use a softer rod with it....which was a lot more fun anyway. I do agree that sometimes fluoro lines can flash light, but I think it happens rarely enough not to worry me. When I have seen it happen in the test tank at home I've never been able to make it do it again, but it does happen. from time to time. But then you can say that about any line except braid.
I had thought about a braid leader to deal with lillies and the like, but dropped the idea as it seemed it was just as likely to cut the fish. There are times when you simply can't let a carp run in the margins and a braid line seemed inappropriate to me.
I do agree about the way time stands still. I've sometimes watched a couple of bits of bread and felt a half hour had passed when in fact it was more like two hours. And when you DO get that bite...........