That's not how view ports work. It's akin to upping the resolution on a monitor, it makes everything slightly smaller, but doesn't infringe on your screen real estate. In fact, technically it expands his screen real estate, because you see more on the right and left sides when you use a view port like that, without losing any of the vertical real estate.
Think of it like 4:3 vs 16:9 for TV's. When they switched to wide screen, you didn't lose any of the vertical picture, you just gained all that stuff you'd been missing on the sides.
I still don't use a view port, because I don't like it aesthetically, but technically it might be considered better to play with one. Look at this video for more info on view ports: http://www.youtube.com/watch?v=fLsb8Cxs8dc. The relevant stuff starts at around 13:09.
Edit:
On the subject of your UI, btw, Neos, I do tend to agree that it's a bit cluttered. I actually show both meters (damage and healing) on my UI, as well; healing because I'm the leader for our heal team, and damage mostly because I'm just interested, but they don't need to take up that much room. Maybe instead of side-by-side, shorten them and stack them in the same space that one is currently taking up. Then you could move that window on the left that has Player/Target with your heals in it in the space the other meter was in.
Don't know if that second black box under that Player/Target window is another chat window, but maybe that can go on the bottom right of your view port instead. I also agree that a threat meter just isn't needed anymore, especially for a healer. The only role I still use one on is when I'm playing a raid tank for swap mechanics.
Another thing to think about is that you probably don't need the micro menu, you can access all of that stuff from their respective keybinds. Also, don't forget that even though you may need the action bars (so do I, don't worry, you're not the only one who can't learn to key bind everything), you can adjust the size of the bars. Don't know if that actually helps you, but it may give you ideas for other stuff if your bars take up less room.
For instance, although I agree that view ports don't hinder you in any way, it seems rather pointless to have one if you still have so many of your UI elements outside of it. Also, remember that a view port is shrinking the stuff that is inside your play window, so unless you're appropriately shrinking all of your UI elements, any UI element outside of your view port is going to cover a larger percentage of your play window than if you did not have a view port. If you could shrink/consolidate enough to get your raid frames inside your view port, that would help tremendously with screen space right there.
All of that stuff is more clean-up and minor things, but the one thing that does very much concern me is the clutter within the raid frames themselves. Between the bar texture, the amount and size of the text, and all the other stuff you need to track, it seems like it would be very difficult to track important buffs/debuffs for things like riptide and dispelling. I would highly recommend using a flat bar texture, and getting rid of the health text. If you really want, maybe change it to percentage, instead of a x/max format, but really I find the bar itself to be more than enough of an indicator for healing. Last thing, I'm also a Shaman healer, and I wouldn't recommend tracking Earthliving on your raid frames. It's such a small contribution to your overall healing, and it can't really be controlled, anyway. The less things you track on your raid frames, the more those things you are tracking will stand out.