I was able to get it working in GIMP. Opened up your bigobs_AlloyLaserTurret.png image in GIMP, changed image mode from indexed to RGB and back to indexed, selecting the proper colormap (otherwise GIMP removes color index 0, shifting all images down one color index), added alpha channel to the layer containing the image, then just selected the neon green background and deleted it. If you already have the proper palette applied, just add alpha channel to the layer and delete the background color.
Edit: Another option for pixel editing tools is MCDEdit - IvanDogovich has a version that allows for working with 32x48 instead of 32x40 images, useful for bigobs and floorobs. It's made with X-Com in mind, so the proper palettes are baked-in.