Huh. I would think, from reading the description, that Background Manager would do what you wish. Did you check with the dev to see if there is something he/you could do to make it work for you?
Or, in my research, I came across this tweak - "InfinityTask" (Cydia, $2.49, USD). I have not installed/tried it, but it claims to "remove 10min limitation of background task." Maybe it'll suit what you want it for?