Seeking advice on mortgage and savings planning

For a little background I'm 40, life in the Bay Area, and my father passed away last month. He left me $350,000 in life insurance along with our combined cash accounts of $150,000 and the house. I also have an IRA of $50,000 (invested in VT). Neither of us have/had any debts, except the mortgage.

This is my home, so I intend to stay here. The rate is exceptional at 2.85% and I know ideally I'd just keep the mortgage and invest the $500,000. The problem is I currently do not have a job (I was taking time off for him after being laid off), and for a myriad of reasons, full time work won't be on the table, but part time will be. I was essentially a Junior Financial Analyst before taking time off and was making $70,000 full time.

My current annual expenses excluding the mortgage are about $25,000. The mortgage is $2,339.60/mo (so just over $28,000 annualized). We're only about 5 years into it, so there's roughly $342,000 of principal and $138,000 of interest.

I'm not seeing a valid path to working part time and keeping the mortgage in place – maybe something along the lines of safely investing the $500,000 in cash equivalents and using the interest to pay the monthly mortgage, but I haven't found a valid path for that.

Is there a way to work part time while keeping the $500,000 or am I basically forced to pay off the mortgage?

Thanks!