This thread reminds me of a situation in a Douglas Adams book, the name of which escapes me at the moment. There was a sofa stuck on a staircase and after trying numerous things to extract it eventually the whole thing was modelled in a computer and the computer eventually decided that there was no way the sofa could have got there in the first place.
Bringing it back to Eastwood Town (bear with me) I could imagine someone modelling all your requirements, the room dimensions and the constraints. Then asking the computer to solve the problem - after hours of computation it comes back with the message "does not compute".
Hope you find a way forward because like so many others your trials, tribulations and successes are all pure inspiration to us amateurs.
John