Fungus gnats are a pain. The adults do not eat much though the larvae generally feed on fungi and organic matter in soil. However, in severe infestations the larvae can feed on roots, causing stunting, yellowing of foliage and leaf drop; they are also capable of transmitting fungal disease. I suspect that you have Christmas cactus root and/or stem rot caused by a fungus. Overwatering and poor drainage can promote both the proliferation of gnats and the disease.

Considering they are heirloom plants, I’m guessing it had been a long time since they were repotted and that perhaps the problem started because your plants looked limp and you thought they needed more water? The overwatering then promoted development of the gnats and the fungus. While limp or wilting holiday cactus can be caused by being too dry, too wet they can also wilt because they are too root bound. These plants generally like to be somewhat rootbound, but can suffer if the roots become too constricted. In such a case repotting to a larger pot or dividing the plant into multiple pots would alleviate the problem.

While you are taking some good steps to save your plants, a few modifications may help with your success. For the cuttings you are trying to root, you should use smaller pieces. Since there is not a functioning root system yet, the plant is struggling to support the large length of stem/leaves. Sections of two to three leaves should be sufficient. Make sure to change the water every few days so that it stays clean.

The same practice of using shorter cuttings goes for the pieces rooting in sand. The shorter the pieces, the more likely the new roots that develop will be able to support the plant. You might also try to root some leaves by laying them flat directly on damp soil and then covering the pot with plastic wrap or a plastic bag to keep humidity high until rooted.   Using rooting hormone on some of your cuttings may improve chances of success. You can purchase rooting hormone at your local nursery or garden supply store.

Make sure that all the pieces you are using are clean and free of any diseased or damaged tissue. Cut away any bad tissue with a clean knife or blade and use tissue from near the top of stems to ensure that they are disease-free. You can sterilize your containers and tools with a 10% bleach solution – rinse and let dry before using.

You can also purchase special cactus mix or make your own mix of 50% vermiculite/50% perlite, which will hold sufficient air and water to support good root growth. I don’t know for sure, but this may be preferable to sand, though sand should be ok. Whatever mix you use, it should be well-draining.

Once you have success rooting, make sure that the potting medium dries out between watering. Good luck! I wish you success!

Here are some reference sites that can give you more detail on best practices for rooting cuttings.

https://hortnews.extension.iastate.edu/how-propagate-houseplants-stem-tip-cuttings

https://www.purdue.edu/hla/sites/yardandgarden/extpub/new-plants-from-cuttings-text-only/

https://wayne.ces.ncsu.edu/2019/08/propagating-houseplants/