How much influence would cooling a landing be at cooling 3 bedrooms attached to it?
Not a massive landing, just would be a cheaper install, rather than having 3 bedrooms done.
I actually have this setup, its what the OP was about. wow it's been 5 years - well the unit is still going strong and I haven't ever serviced it or anything so there is £500 saved so far. He wanted £100 per year and as covid hit I never got it done, then never got it done.
Anyway to your question, it works great in winter as a heater, absolutely bakes the upstairs for cheap.
Summer, well it works "enough" I have to use a fan to direct the cold air but it keeps a bedroom ~20c no matter how hot it gets outside, (you gotta pick 1 bedroom haha, cant do 3!) but as others have said a huge amount of cold air just drops down the stairs so it's incredibly inefficient. Like you are thinking I did it purely for cost saving reasons and if I could go back, yeah I would 100% pick a bedroom and have it in there, There was just no good wall to mount it in a bedroom for me and I would have needed a pump for the condensate and I was concerned about the noise of that kicking on and off. (neighbour has actually complained about the noise of the outdoor unit so im sure if there was any noise in the attic overnight, I would be getting a lot of aggro from them)
As it's actually used as a heater 80% of the time, I think I got away with it, and during these little heatwaves, it makes a room perfectly cool enough to not even notice the heat.
tldr - absolutely pick a bedroom and have it in there.
Oh also! super important!! - if you have it installed to a landing (small space) and say you set it to 18c it will cool the air around it'self very fast and start throttling down, whilst in reality the bedroom your trying to cool is 25c haha. Does that make sense? it's so far away from the room your actually trying to cool, its cooling the landing then feeling smug it starts throttling down the compressor, meanwhile your sweating your balls off in the bedroom! It's not taking its room temperature from the bedroom into consideration, its taking it from where its installed.
THANKFULLY (and kinda annoyed the installer didn't explain the above to me as I would have gone straight for a bedroom install there and then) my remote control for the AC has a function where it can beam the temperature for the AC unit, so whatever room the remote is in, it beams that temperature to the AC unit, so the remote stays in a bedroom and it keeps the AC blowing cold air 24/7. As its reading the temperature of the bedroom not the landing, if it didn't have that feature I would be **** out of luck.