I was wondering if you have the funds to pay direct or are you reliant on the State in providing the funds for a caregiver. I know that makes a big difference when you are trying to hire caregivers.
My friend is dealing with a similar situation right now because the State will only give her 31 hours of caregiving and she must accept the providers given to her by the company that has a contract with the State. For the other hours she requires during the week, she hires people from Care.com and pays for them herself. The only other option she has is to go into a nursing home situation to get round the clock care and she wants to avoid that scenario.
Have you considered moving in with someone who is also disabled and share caregivers? Because then the caregiver will earn more money because they are caring for two people versus just one. That is usually a good enough reason for them to make the house call everyday. It is always about the bottom line for most caregivers.