An important information is missing from my paper under review
Since it is a crucial piece of information that alters the content (and possibly the result) of the paper, the most fair would be to contact the editor and explain the situation so that the reviewers (which seem that did not catch the missing piece) make a better and more informative decision. 

The new version should be refereed. I think just adding supplementary material on an accepted (but possibly flawed or at least weaker) version is not suggested.

So: Contact the editor. S/he probably let you submit a new version which will go to the usual review channels, probably with the same reviewers. As for the page length, probably you will have to squeeze in everything, which means a lot of re-writing.