Seeking advice on in-home care for elderly mother

My 96-year old mother lives alone in her 3-bedroom home in Berkeley and is not open to living elsewhere. She has mild cognitive impairment and sometimes needs help with cooking, bathing, and reminders about taking medicine, changing clothes, etc. She's oriented, and can read and converse. She does not need physical caregiving. 

If she pays caregivers for 24 hours/day it costs over $220,000/year. We're trying to figure out how get the care she needs without spending so much.

One idea is for her to pay daytime caregivers, and find a responsible person to live rent free in her home and provide limited nighttime care, which means checking on her 1-3 times/night. They'd be in the Elmwood area and would have a bedroom, private bath, office, and shared kitchen and backyard. Start and end times would be flexible. Her daytime caretakers are present 9am-9pm, and she is okay alone for limited periods of time.

Do you have other suggestions for ways to handle this? If the rent-free idea sounds good, do you know of anyone who might be interested, or have suggestions about how we might find someone?

Thanks!