On mg discount site I've managed to find a single slot rx560 4gb which will get the job done in terms of performance. I have to give amd credit this card is really cheap in comparison to that of Nvidia. The card might some thermal limitations but in theory everything should be fine!
I have found a half height bracket which fits around the io (display port, hdmi and dvi) which means that in theory everything should be good. Thanks for your suggestions!