Plenty of ideas here, but my personal favorite (for it's simplicity) is using condensation to lower the pressure. I am not sure how low you could get with this setup, but I would suggest the following:
* Fill the chamber with steam. This is probably easiest to accomplish by pouring in a small amount of boiling water.
* With lid still in place, cool with cold water to condense the steam.
* Remove the cold water and add the dry ice. This should remove any remaining water vapour and freeze the water at the bottom, so the humidity should not be too different.
To increase the effectiveness, you could add a small vac pump (e.g. vaccuum cleaner or from a diesel) to reduce the pressure before chilling, but this will also remove some steam... It'd take some experimentation to ensure it would get the pressure low enough. You may need to try a different refrigerant, too, but if it works it's definitely the simplest option...
One other option I can see... Take the chamber, with a one-way valve installed (in place of the vac pump) to a hypobaric chamber. They take the pressure down, then when you take it out it's all set at the required pressure, ready to chill and fire.