the slate table wax, comes in a solid block form and must be heated and melted and then poured into the seams and flowed out from there, then as the wax hardens, you shave the wax to a perfect level and the wax is then solid again and will not move or leach.
If this type of wax was not used, then there are many, 'bees waxes' that could have been used and laid onto the slate, and then smoothed out like lathe and plaster or a dry-wall job and it might look perfect initially, but when it comes in contact with the cloth or felt, then the other components in the wax can leach into the bed covering and leave marks and dark spots as you have mentioned.
As to the solution, if it was a quality high end, like gornita or simonis cloth, then you might be able to remove the cloth and clean with a cleaning solvent of some type and re-install, but I cannot guarnatee the results and you should contact the make of your bed cloth for cleaning products that are successful.
Hope this helps, in the future, if you are not positive, I would go with a professional, the cost to install is minimal if you figure the amount of enjoyment you will get with a top-notch professional installation and finish, just my opinion,
Good Luck
Mike 'acedonkeyace' Kennedy