How to change time signature without changing rhythms?

So I was writing a piece in 6/4, but I think subconsciously I was writing it in 4/4, because when I went to play it back with the metronome, it sounded awkward.

I am lead to believe that the section ought to be in 4/4; however, doing a simple time signature change doesn't actually rewrite the rhythms to fit. Instead, it keeps written note value, thus not being in time with the measures (i.e. a dotted half note in 6/4 stays a dotted half note in 4/4, even though, within the context of the time signature, they are different).

Is there an easy way to avoid this problem? Or do I just have to buckle down a rewrite everything in the correct meter?