Is there any chance that MD5's compression function can be represented in a completely different way so that it's much easier to compute/reverse it?
Not that we know of.
Although we have no proof, there is still a strong belief that MD5 represents a one-way hash. It is broken, but that doesn't mean we can reverse it (or the compression function that it is based on).
Similarly, we don't know a faster way to compute it (in the algorithmic sense) but we cannot proof that there isn't a faster "representation".
One of the things to consider here is P versus NP. As long as this remains unsolved we don't know if P = NP could hold, which would have interesting consequences.