I have mild hyperhidrosis and though I don't suffer from body odor I don't like that any physical activity causes me to sweat and I find that deodorants can irritate my skin pretty badly. So I researched different solutions for antiperspirants and here is what I found out:
this is like your basic deodorant, though you can get stronger versions of it for use across your body. This basically works by irritating your skin to close the pores.
this is a treatment with electric shocks, and it won't be practical for your back.
Injections and Surgery:
Botox injections and surgery (usually to cut certain nerves) is a relatively new treatment but can have harmful side effects (including even more sweating).
: There are pills you can take to reduce sweating. I used to occasionally use a glycopyrrolate pill (Avert is the brand I had bought, but that was years ago) and I can tell you that it worked much better than anything else for me. The side effect was dry-mouth though but they worked very well as an antiperspirant.
For your type of sweating this is what I would recommend, and it is available over the counter (I can try to dig up where I had bought it if you want).
Right now I just use regular deodorants, but they still occasionally irritate my skin, and while there is no perfect solution I thought the glycopyrrolate came close during the time that I used it. Right now though I just switch up between mild deodorants when they start to irritate my skin.