Hello!
I've been trying to figure out the location of the sick room for a long time, and I have an idea (probably feeble, but what the heck...). First, I noticed in a photo of Alexei's bedroom showing his dressing table between the windows, that the curtains look like the ones in the sick room. I got to thinking: I believe that his rooms were remodeled late (1916?). If you look at room 16 & 17 on the plan---his bath and cinema---and take out the bathroom and look at it as one big room, then the configuration is correct for the sick room. The door midway on the long wall, the stove in the corner, and the window and door in the opposite corner, where there is a picture of Nicholas sitting by the sick bed. What I wondered is, could that have been the sickroom, and then changed in the final remodel of Alexei's rooms?
I hope that I make some sense---just an idea, anyhow!