I have no idea how to link to it but if you have a look at the thread Cat Litter Trays started by poiuytrewq on 19th Nov there are some suggestions which may help you.
Same problem! Two stair gates later we still
Have the same one I have to remember to open the gates overnight though or one cst won’t use it.
I am still planning to sort something out.
I like the idea of a bit of furniture with a cat hole/door allowing the cat in but not the dog