And YET gravitational time dilation maintains that TIME is not constant. Therefore the denominator varies making the whole formula change. The length of a second is different depending on the gravitational forces in play.
Relative time is not constant. And you don't seem to get it: the speed of light in a vacuum (space) is unchanging. There is no formula for the speed of light because it is a constant.
What the heck does E=mc^2 have to do with the time dilation affecting the speed of light? If m or c varies then so does E. Where is the problem?
It has to do with it because c is the constant in the equation? A constant cannot be changed; it is a fixed value.
Time dilation is what happens to an object as it approaches the speed of light. The closer to that value, the greater that dilation. It can also occur due to gravity, as you said. If you really want the answer then this site states it more eloquently and clearly than I can.
"speed of light" in a vacuum, such as in space. When it does so it travels at 300,000 km per second (186,300 miles per second). At that speed it can travel around the world seven times every second. This is undoubtedly very fast indeed, but in terms of the size of the universe it is still, perhaps surprisingly, very slow. For example, it still takes light around 1.5 seconds to reach us from the moon, 8.5 minutes to reach us from the Sun, 4.25 years to reach us from the nearest star (apart from the Sun), and about 14 to 15 billion years to reach us from the furthest objects yet seen.
A million or a billion years is a very long time, of course, but perhaps we're forgetting something. We are measuring time with our own, Earth-bound clocks! Relative to most objects in space our clocks can be considered to be very near stationary. So how does a photon travelling at the speed of light experience time?
If you look into a clear night sky at the right time of year (winter in the northern hemisphere) you will see a pattern of stars that looks like this, called the constellation of Andromeda:
The object shown as M31 is called, for obvious reasons, the Andromeda galaxy, and is rather like our Milky Way. On a clear night you can see it as a faint chalk-like smudge in the sky, and for most people it's the furthest object it's possible to see with the naked eye. Pictures taken with powerful telescopes show it to be composed of millions and millions of stars, many of which are just like our own Sun. The Andromeda galaxy is so far away that it takes the light from it, as measured with our Earth-bound clocks, over two million years to reach us. However, a photon emitted from a star in Andromeda and heading out towards the Earth travels in a vacuum and, because it's a photon, travels at the speed of light. Because the photon is moving at the speed of light it has a 100% time dilation factor. To the photon time does not exist until it strikes the upper atmosphere of our planet and even then is only slowed down by a tiny fraction. According to a photon in free space, time, or for that matter distance, has no meaning whatsoever, and it gets from wherever it is to wherever it is going instantly! Personally, I'm happy to admit that I find that mindboggling..."
http://www.emc2-explained.info/Time-Dilation/#.VlETOl9OKnM