I probably shouldn't have taken the scope apart and cleaned the primary mirror without checking this first (...)
Well, I might agree with you here. Unless you know what you are doing and have significant experience working with optical instruments, there is a very good chance that the alignment of the system is messed up. And that the mirror coating is damaged. Our local astronomy store (now gone) used to have a star diagonal whose mirror had been 'cleaned' by its former owner. It was perfectly fine, ended up completely ruined. They used it as a cautionary example.
But many of these big dobsonian telescopes do indeed require some extension tube. This was the case for a 10" Sky-Watcher dobsonian purchased by a local club here. Took quite a while for them to figure it out because they were always trying it at night.
All you have to do is to look at something far during the day, like the top of a communication tower, and see how the whole thing works. Good luck!
--Christian