Ah my good friend Jhoanna's shining role. Always love seeing her in that.
I'm the guy that will always have a slant towards the simple, classic... and doable. I tend to stray from hardcore CG for this sort of thing, but not from film techniques or tricks in general.
I'm coming at you with less specific movie examples and more general ideas, hopefully still valid.
Remember one of the most famous, and powerful, examples of all time is simply turning your film from B&W to Color. The opposite could be used as well.
Another great option is to Shoot with your characters blocking their scenes and running their lines as fast as they can, double time if possible. Then slow down your footage in post until its perceptually about normal speed and use ADR or time stretching (with pitch intact) to create a completely surreal effect. Again the opposite works as well.
I (again being a weirdo) found the continuous spinning top far more powerful and creepy than any of the big budget effects in Inception. A small almost subliminal slight bend of the laws of physics type thing can go along way for viewers. Something that just feels "off".
If you are OK not beating your audience over the head with the alternate reality an exclusive dutch angle or low Kubrick angle could give an uneasy, anxious or even slightly annoying feel to an entire scene.
Another cool trick is to lock your tripod and shoot a plate of a forest background, then move the actors into place and roll the scene (works best with minimal or at least normal actor movement beyond dialog). Then in post mask them onto the forest (you can be really rough with your masking since your actors were also actually against the same forest). Then the trick is to slow way down, or even stop, the plate shot so the trees aren't moving. Oh and zero foley. Then when they "exit the dimension" let the plate roll and dump in a nice wind.wav -- Some people may not even catch this, but they'll feel it.
Interested to know what you ultimately decide upon.