Fragment the piece so you are only practicing small sections at your desired tempo. Also try practicing sections outside of chronological order. Following that play the piece as written, and see if you can decipher if any parts of it feel different or inconsistent from what you were doing in fragmented practice. If any such portions remain, these are the parts that are causing tempo fluctuations and require focused practice to iron out. Look for parts of the piece that cause technical uncertainty, or lack of mental clarity and direction.
Practicing the piece at different tempi would most likely be a good thing, as one has a basis of distinguishing between differences in tempi and will thus have a basis for recognizing the phenomenon and correcting it when it fluctuations are undesirable.