azza, eyeballing the stem on your bike, it looks like it might be 100mm, not a lot longer. What is its length?
Like I said, try moving your seat back a bit, plus rotating your bars forward, and you will increase your reach by probably a couple of cm's. Do it mid ride and at least you will see feel if it feels better for your back from getting a bit more stretch out.

stems come in a whole slew of lengths and angles, so there really are lots of options out there if you go that route, or find that the one you ordered isnt right.
I would add too that I'm sure a lot of folks are like me and have a small collection of spare stems around from changing them out on other bikes, its a fairly common thing to have to do.