Change the 'height' of a World?

Okay, so let me put in some details in first.

A long time ago, I created a new Creative flat world using the Miners dream Preset. It was great and obviously the 'stone' was way too much, at first it was just a stupid messing around world, you know, your average player TNT'ing his way through the depths until he reaches bedrock. Anyway, then I started building a few houses and pixel art and command blocks, and replicas and God knows what else. Long story short, the world is now my most prized possession (after a few other worlds). But theres a problem.

Problem
1. The world has a quite small maximum height.
2. Ever since the "closer to the clouds you are, the more snow you get and vice versa for rain" thingy, when even its supposed to rain, it snows and covers the whole land -_- which is ugly.

Solution
Here what my first solution was.
I would open up McEdit, remove all the useless stone underneath my creations, select my creations and drag them closer to the bedrock and hence away from the sky! Voila! But then I thought that, even if I did that, the new chunks that I'll eventually generate, will be back on the same high level.

Second solution:
I select and copy my creations, paste them unto a new flat world. But his is long, and some of my creations have huge basements, it would most likely fail for me :/

Now Im stuck, help is appreciated