Nigel Ball and Tony Marsden know a lot of stuff about this area, so they may be worth consulting, especially on the Springfield resurgence. It wouldn't surprise me though if this were natural drainage from Moss Rake. Nunlowend Sough drained Long Rake, which is not far north and more or less parallel, and, merged with the flow from Kronstadt Sough, crosses under the road at Brough House. So another outlet between Nunlowend and Bagshawe, natural or manmade, and draining either vein, could well be possible.
I don't think much work has ever been done dye-tracing Moss Rake or Long Rake. Partly as there are no obvious water-flows in the mines higher up the vein apart from Rake Head, and that funny waterfall in the shaft. That could be tested, but requires sneaking around, which may not be a good idea at present - as also discussed at Bradwell Symposium! The main working areas and natural caverns in the Moss Rake mines line up with the main beddings in Peak-Speedwell, so it may be possible to infer a resurgence from the dip of the beddings and the intersection of the vein cavities, but I don't have the time or knowledge for that. There is also the 'Moss Rake Sink', at the road junction entrance to Sidebottom's quarry and Hallam's Venture mine, but I have no idea what kind of 'sink' it is.
There is a place nearer the village that could be a candidate for a 'general' test, as it's on the downstream line of Moorfurlong, but that's a dirty surface hole, and very much private, so may not be much use. But I could ask, as a tap wouldn't be far away!
Also, what about leakage from Pictor End Sough? Is that possible?