My concern with the washer things is that the plaster in traditional lathe and plaster surfaces is very different to modern gypsum plasters. It has fibres in it to strengthen it (usually something like horse hair) these make the plaster elastic hence it is currently sagging rather than flaking then falling off. What you may find with the washers is that they only support a small area around them and the problem will continue where there is no washers. If this is the case you'll end up with a washboard look with sagging between the joists.
My concern with the washer things is that the plaster in traditional lathe and plaster surfaces is very different to modern gypsum plasters. It has fibres in it to strengthen it (usually something like horse hair) these make the plaster elastic hence it is currently sagging rather than flaking then falling off. What you may find with the washers is that they only support a small area around them and the problem will continue where there is no washers. If this is the case you'll end up with a washboard look with sagging between the joists.