I can see why your sparge drains slowly. I mash in a 13" diameter cooler for 5-gallon batches and my grain bed is usually about 5 inches/13 cm. I stir my sparge water then recirculate until the wort runs clear before draining. It drains quickly - never timed it, so I can't tell you how many minutes in a "quickly". Your grain bed must be at least 25 inches/60+ cm. It could be a major challenge to stir that deep and would take longer than mine to drain through such a long column of grain.
In fly sparging we assume the water trickles through all the spaces and carries off most of the sugar. In batch sparging, I've always viewed it as me forcing contact between the water and the grain, allowing the grain bed to settle, then draining off the sugar-water. If you can't stir that deep grain bed, you have to hope the water trickles through evenly and brings most of the sugar with it. I'd suggest at least trying to stir as deep into the grain bed as possible, recirculating til clear, then draining. As I'm trying to visualize this I'm seeing a 25-inch grain bed under 10 inches of hot wort; that's going to be a major challenge.
This link may help with one approach to batch sparging. Denny uses a rectangular cooler, so his grain bed is MUCH thinner and easier to stir. He recirculates by hand.
dennybrew.com
Please, let us know how you solve this problem.