Keep the leading, maintain the grid, don't fret the variable length. Fear of open spaces is a common phobia, conquered by maintaining steely-eyed discipline and repeating "White space is my friend" twenty times before breakfast each day. :)
Different-sized blocks of actual text are are a natural consequence of the length of the copy. As a result, the reader will seldom give them any attention. Varying the leading (or anything else that radically changes the type color), on the other hand, immediately draws attention to the typography. That's bad, because in a situation like this typography's job is to be unnoticed, not to be a feature in itself. You can tweak -- small changes in tracking or leading can help a paragraph sit better on the page, for example -- but anything more than that becomes visible to the reader and is a no-no.
The same principle applies when you have too much copy. The two common approaches to this scenario are 1) use the copy as given and change the block size, or more commonly 2) copyfit: edit the copy so that it fits the available space. Neither case involves highly visible changes to the typography.
Where you do have a design challenge is the border. I would get rid of it, almost certainly. It's very unlikely to be a useful design element.