I would resist notching joists as it will make them weaker. You can but Joist Hangers from B&Q or screwfix. Not sure if that image will work, if not you can search screwfix for 'joist hanger'. They come in different sizes to suit the current joists. Then you add a new piece of joist or just some 50x50 timber to the new joist holders. Its a little over the top but its better to be safe than sorry. They are only about £2.65 each so only cost about £13 including timber and screws to make 2 decent fixings for the screen. You could also use Speedy hangers (screwfix search) I guess B&Q or another decent DIY shop would sell them.
I once made the mistake of not doing a proper job on hanging a screen, only to have it jump from its mountings and land directly on my Sky box. Result 1 crushed Sky box and 1 bent screen!!!!!
So dont use any hooks, make sure you use eye fittings with d shackles. Make sure the screen cannot under any circumstances come off the mounts. Bass has a habit of vibrating thinks loose!!
PS I'm not a builder but I have a damaged sky box and a slightly bent screen because I used 'S' hooks!!!