Because it's a large bed what I would do is place it in the bathtub or something large with perhaps some warm water, let it soak for a bit with the help of someone of course to move it to such a point. If you can, let it sit at least over night to soften the dust and any debri that might reside from the natural state of the crystal bed.
Use a very soft toothbrush to gently rub away the dust that has settled on it over time. Because of the state it is in don't force anything down between the crystals at all as they may break off.
Another thing you could do is if your water is too high in cholorine is to get some spring water and soak it in that or gently pour spring water over it to loosen up the dust. You could even turn it into some sort of healing session perhaps?
Use a very soft cloth to gently soap up and dry any excess water that might remain on the crystals themselves.
I just cleaned several of them this way over the weekend with not too many issues. Some of mine did flake off but that is natural because it is drying in the air. Crystals in general are used to either being in a Geode, which is what you have perhaps, underwater of some type or in a very moist damp and dark cavern. Air dries them out especially if your home is very dry.
The problem with large beds like that is that debri get's down in between the cracks of the crystal and it is almost impossible to clean them out manually which is why I use warm water. Don't use salt in the water even though it's a cleansing agent, it will only prove to dry out the bed more. In fact I never use the salt cleansing method on a crystal bed, I cleans it with Reiki (outside of manual human cleaning).
Perhaps from time to time when it does flake, save the flakes and put them in a small dish somewhere else in the house if they are the crystals themselves. At least you'll still get use of them.
I think you have the Reiki cleansing part down fine, you just need to rid it of some of the world debri (dust) that occurs. I think you'll find you'll get many wonderful years out of your crystal.
Good luck!
Barbie
