Thanks man!
Yesterday I followed Celestron instructions to the letter:
Pointed the wedge towards the North with a compass
Performed an EQ North alignment (I used the two stars method)
Done a polar alignment adjusting the wedge instead of using the directional control
Re-done the EQ North alignment
At that point, I noticed that my StellarMate was acting out after an update - couldn't connect either with VNC or SSH. So I missed my chance to check how good my polar alignment was based on your instructions...
I had spent 2 hours doing all alignments so I decided to take some pics anyway with the DSLR camera (this time with the light pollution filter). I pointed the scope at M81 - without any indication on the accuracy beside what Sky Guide on my phone was showing.
I was very much out of focus, but I didn't notice on the spot. Looking at the glass half full, at least I have learnt how to do a polar alignment (hopefully it will become faster as I go), and I have taken a mental note to check that all the equipment is working after any update.
Now I also know that the laptop's battery won't last long enough if StellarMate doesn't work.