Hi frogga,
You don't say what the shift involves in practice. I'm just guessing here, but assuming the confidential bit is the time you spend with the "client", (counsellee??) and discussing case details, then all the other activities are done in private to a lesser or greater extent, anyway - going to the loo, eating, etc - well, I do most of the things on your list in private, normally

. If that's right, could you ask to have your carer with you somewhere out in the "office" area, but undertake to meet with the people in need of counselling, and have case discussions, on your own? Could you manage that? Then you and your carer could manage your own care "behind the scenes" in between seeing clients and supervisors - actually, that's how people with no disability would do it anyway. I'm thinking that a compromise should be possible.
I see why they need confidentiality, because the "clients" do need it...I would have a big problem going to see a shrink with someone else (who is there for their benefit, not mine) in the room too...I'm just looking at it from their point of view for a moment, you understand

On the other hand, if the "clients" are told about the situation in advance, and agree to it, then that's another story.
Also, they might be able to come to a compromise regarding the length of the shift, and duties required. Perhaps if you spend more days/weeks there than they stipulate, but take on less per shift, or take longer breaks...maybe something along those lines.
If they won't take the hint and talk to you about it, then you will have to talk to them.......they must have, er...noticed..maybe they already know the answer, just haven't spoken to you about it yet - or think someone else already has... I really do hope you can resolve this, though, you'd be *really* good at it!
And, BTW, without wishing to relegate you to a stereotypical predefined "role", I can see a huge need for someone with disabilities in need of counselling to speak with someone like you - (bet there just aren't that many - are there even any, with hurdles like these to negotiate?) - there's nothing so reassuring as talking to people who've been through it all themselves. Bit like this forum
all the best!