I'm sorry about your mother's dementia. I'm sure she will get the care she needs at this facility and, importantly, your family can have the support you need. I believe your mother's financial situation is better than many her age, but the cost of her care is significant compared to her assets.
I put the following into Firecalc:
Sending: $78,000
Portfolio: $675,000
Years: 14
Other Income: $18,000 (social security, starting this year)
Portfolios with 50%, 75%, 85%, and 100% stocks are successful less than 66% of the time. I used 14 years because actuarial tables put the life expectancy of a woman 75 years of age at 12.9 years. I think you actually should plan for 20 years. At 20 years, FireCalc doesn't provide success rates above 50%.
So I think you should plan for the eventual possibility of your mother's funds running out and transitioning to medicaid. Check into the assisted living facility's guidelines for residents switching over to medicaid. Many continue to provide the same standard of care to someone who came in as a cash payer and needs to make the switch.