I've got the basic mechanics up and running; you can download it for yourself
here. A screenshot of my ugly placeholder graphics:

Keys are:
cursors: movement
z,x,c: pickup items/use items.
space: interact (open doors, speak to people)
And for debugging:
b: display bounding boxes (red = collision boxes, blue = player's pickup zone, green = authority figures' sight zone)
1,2: switch between the two locations (present, future)
t: trigger a nurses' tea break (this and the location switching will be triggered at particular points in the final version's song)
When a nurse spots you doing anything untoward, he'll run over (or try to; they're not particularly smart) and force feed you more drugs. The more drugs you have in your system, the harder it is to do anything. The doctor's drugs are twice as powerful as the nurses'.
Feedback would be most appreciated (especially re items, and potential chains of actions you could use to kill the doctor and the nurses). At the moment it feels like I'm going to have to add a lot more stuff (items, events etc.) to make the randomness actually work and give the player a reason to play the game more than once.