Thanks for the replies! Right after posting I was so fed up that I went to that "auto care" shop in Blackpool shopping centre (on the right before entering Dunnes stores) and I asked them to fit the radio.
The guy came, saw the situation, then shamelessly forced the ISO fitting frame in, checked that the radio was working and took 30 quid for the 5-minutes job.
To my great surprise, it did actually fit that way, and it seems stable enough.
I'm still astonished for how simple it was and for having assumed that the frame would have never fit that way.
I think I'll buy the brackets and get a proper fit, but for now it will stay like that.