This young person's parents and other caregivers might benefit from: 1) Respite - even a weekend a month 2) If two or more caregivers are involved, it may help to brainstorm on ways for them to trade off. Even an hour or so away can be a big sanity saver. 3) Training, formal or informal, on stress management methods.
If one communication function of the "pica" behavior is essentially "come over here now and pick me up", the child could be taught more "appropriate" means of obtaining this desired result. It seems to me that Brian Iwata (or one of those types - Joe Richly at the University of Minnesota perhaps) has done a lot of research on similar patterns. You might instruct the caregivers to respond immediately when the child makes a move toward the drywall (or whatever). Phase one could include a day or two of just that. This may show the child that his communication is not being ignored which may in itself reduce the rate. Phase two would pair phase one with modelling a simple "appropriate" response such as waving one hand while giving hand on arm guidance and then immediately picking the child up in a rapid fire fashion so that the response is still paired closely with the result. Phase three might fade the physical prompt gradually, hopefully shaping the desired response. Explain to the caregivers that the hope is that their intensity of attention to this training should go down as the child learns that he will consistently be responded to.
As I suspect you would tell others, my advice is designed only to provide possible direction and is given as such without knowing enough to say what I would actually do. Joe Richley studies, if I remember right, would provide more clear direction regarding communication training. I do believe that it is never a mistake to look at communication function first.