First time running serious hills on my new bike. Small chainring, and largest rear cog for the main climb. Once that had levelled out and before the next climb I went through the gears to a smaller rear cog and found a load of slack (probably more than what the OP has shown).

Solved by tightening the B screw, which took up all of the slack. As an added bonus, turns out my pulley and cog were too close together and my chain was getting pinched in the large chainring and largest rear cog. Now this is also solved.

Not planning on cross chaining for long periods but in amongst climbs it's better than double shifting.