Sizing aircon

You need to do detailed heat calculations like people used to for central heating when the installers understood the physics behind what they were doing.

I've done a couple of rooms, and the biggest input was sunlight through the windows in one case (and would have been in the other case if we hadn't got the windows mirrored to keep the sunlight out of a small business computer room).

I may be out of date now, but 9kW (pumped, not power consumption) was the smallest split unit around 10 years ago, and given you are north facing, that should be more than enough. You should also look at insulation - e.g. radiating heat in from hot lofts is a common problem, and having good loft insulation and/or loft ventilation can help with this.

For people comfort, reduction in humidity is much more important than the drop in temperature (although a dehumidifier is unlikey to help due to the extra heat output from it).