You have set up a non-sequitur, visually.
This is a teaching moment. You're going to learn a lot with this exercise. This is portfolio material to be sure. It's definitely a "How to do it" tutorial.

Here's what you're up against:

As you have correctly concluded, a silhouette is back lit. Transparent liquids will show as "dark-line" when back lit. That is dark against a white background.

Frozen, the image of the droplets will be high contrast. A time exposure will allow the light background image to "drown-out" the dark droplets against the light. The result will be seen as an average "grey" for the moving dark droplets against the nearly-white background, if at all. The fix is to use a faster exposure to hold the dark-edged droplets in the mist to resolve themselves retaining contrast.

However…

Front-lit transparent liquids show as "white-line" when photographed. That is white against a dark background.

Combining the dark-line back-lit image with a white-line front (or oblique) lighting begins to cancel-out the effect between the two "contrasting" lighting techniques. In effect, you are trying to show white-on-white and thus balancing the effect of one will negate the other. The long exposure will diminish the silhouette effect of the mist.

Conclusion: You have a VERY delicate (light) balancing situation.

Comment: Be kind to your model and use a mannequin to set up the lights or she will look like a prune when you're ready to take the shot.

Tip: The reflection from the shiny tiles behind the lights can be killed with a drop-cloth or curtain to catch the spill and absorb it. The light you're using for the silhouette placed in front of the glossy tiles will still be effective for providing the background illumination for the silhouette effect desired.