I am one of those who can't quite do the fresh look when walking in the heat - I am a red faced, puffy, sweaty mess (but very happy!) and my back gets sweaty. It did with my Osprey Aura, with an air flow gap - though it felt amazing, my back was just as sweaty - and it does now with my Osprey Tempest, which sits closer to the back but has a ridged and mesh covered back panel. You have your pack already so re-investing in a different one is probably not what you want and it might not even help that much. You say your back sweats uncomfortably - could it be that your choice of top adds to the dicomfort? If you walk in synthetics, could you try wool or a silk mix or vice versa? I found getting sweaty in my clever sun protective shirt was a lot more uncomfortable than in my merino T-shirt. I take it you are not wearing cotton, which soaks up moisture and holds on to it. Going for a walk with a top in a different material might be worth a try and works out cheaper than getting a different pack.
(That said, you still have time to to so and get used to a new one if you decide to do so.)