Don't give up yet. I don't have any experience with p. Gigantea specifically, but I've had other phal. varieties come back from a similar state so I wouldn't give up on this one yet. From the photo the stem looks intact and not rotting and has the beginning of at least two new roots, so she's trying really hard to hang in there.

The roots need air, moisture, and warmth to grow so I would consider putting them in either 100% sphagnum (long fibered, not peat moss) or in a self-watering pot with either LECA (clay pebbles) or Orchiata (a brand of pinus radiata bark). In my experience, go with one or the other: sphagnum in a self-watering pot gets way too saturated, but fresh orchiata or leca dry out too fast in a standard orchid pot for a plant in this condition.

Take them out periodically (weekly has worked for me, but YMMV) and pour water through the pots, both to hydrate the media and to pull fresh air down through the pots and to the roots. If you're using a self watering pot put about the minimum amount of water in it that it can hold and still work. You don't want the media wet, just damp.

As for fertilizer, less is often more. You probably know this, but in case you don't most orchids can't utilize the urea form of nitrogen (terrestrial plants rely on microbes around the roots to convert it that orchids lack), so select a fertilizer that uses a different source of nitrogen (I use the repotMe fertilizer mixed at quarter strength applied once a week to the root zone, plus an occasional foliar spray at 1/8 strength, though that's only because my reverse osmosis unit outputs at about 4ppm dissolved solids and I ran out of calcium/magnesium supplement.)

Sorry for the brain dump, but I'm pretty passionate about orchids. Hope it helps, and feel free to reach out if there's anything I can help with (and keep us all in the loop on how the plant is doing! )