Have the care home staff checked for any infections? Have they tried pull-up incontinence pads on him? Have they checked whether he suffers from constipation, diarrhoea or overflow? Whatever is ailing him clearly distresses him but a good care home with the help of a doctor would get to the bottom of this instead of moaning to you how much of a problem it is. It's their job to deal with difficult people who can't help their disease but deserve compassion and help when they are clearly in distress. Instead they are distressing you as well. Tell them to get a doctor out to check him over.
I would agree with you that the care home should be doing something rather than moaning, but essentially many ordinary care homes are just not geared up to deal with this sort of behaviour, in terms of both number of staff and the skills involved.
My father's dementia care home was pretty good, but when he started urinating inappropriately and faecal smearing, (plus aggression towards other residents) they could no longer cope. To be fair, care homes have other residents and staff to consider, and essentially this level of behaviour is beyond their scope.
(Incidentally, he was self-funding, Merlot, so I don't think your husband's care home should be 'blaming' the LA for not paying enough - and anyway LA funding is always less than the self-funder rate.)
My father is now in an NHS Dementia Unit, with specialist mental health nurses and a ratio of 1 to 3, funded by CHC, and this is what I think Merlot should push for. From her brief description, her husband is similar to my father who scored 'Severe' for Behaviour and Cognition, and was also unable to communicate.
Although my father does require 2-3 nurses/carers for personal care due to his aggression, the faecal smearing does not seem to be an issue now, mainly because of the skilled staff and their ability to pre-empt such behaviour. Just having more staff means that patients are changed more frequently and are not left soiled for too long anyway. Also, almost all the patients wear trackpants with ties and/or belt secured tightly round the back so that they are unable to pull them down. This and other practical measures - such as having lots of tactile 'toys' available to satisfy the urge to fiddle with something - make a big difference.
Merlot - these ideas might be worth a try, but if I were you, I would push for a CHC assessment with the aim of getting your husband into a more appropriate level environment to cope with his needs.