I've never seen the situation you're describing (unless I engineered it myself, in which case I've probably prepared ahead of time), and draining what is clearly a refilling system is going to be a bit troublesome.
But what I'd try to do is to edge-drain (set up fortifications in edge-tiles, a number of them in small bunches, you can perfect the design for each new iteration - and always arrange this with all due flood-friendly pre-planning/control[1]) or perhaps find a lower aquifer to permasink into.
Hard to be definitive from what little I know, and it could be that your pump philosophy is the right idea, too, but not quite applied correctly.
(If it's not replenishing water, you could also try a massively multi-well draining project. Mandwarfpower-intensive, but visually would be stunning. Hopefully not dwarf-stunning, but I rarely have well-accidents so I'm not sure if I'm just naturally averting the usual reported problems.)
[1] Easier to show than explain, but I can't do it and screenshot it right now, so Explain it has to be... Dig right up to 'breakthrough' but not yet, along a length. Set up floodgates along that final wall. One option is to have two levers, each controling alternate floodgates. Set up a 'chequerboard' of pillars in the space this side of them, for pressure-anulling purposes, open the gates to that continue that pattern onto the wet wall. Set to Dig/Ramp/Smooth-And-Fortify one of the gaps (whatever process you want to use to breach, but I recommend the SAF one for several reasons) and as the dwarf is starting the breach unpull the lever. The floodgate will not close until he moves back, either when taking a break (in which case re-pull to let the job restart), he's finished and moving away or he's finished and gets swept by water. The closed floodgate secures the area. Build a new retaining wall in his direct escape route(s) so you can repull that floodgates-lever to try the next(-but-one) along. Repeat-and-rinse... When you've got those done, clear the damp-dampening walls out, prep the wide-enough drain from this area, remove any remaining debris, get out, seal up, open both sets of floodgates... Experience FPS drop, but (with luck) also that of the water-level. No dwarves need to be drowned (or FBed) in the process. Always possible that errors or other adverse factors will (possibly because I forgot some detail of the process, which I've also found useful for magma-tapping but with a slight chance of burns if I'm in a rush where wet feet wouldn't be an issue in this case).