$750,000 is a lot of money. I have a job that pays me well, and maintaining my legal, safe lifestyle is worth more to me than getting away with more money.
I would search for anything that helps identify the owner, and failing that, confirm my idea with a lawyer. My understanding is that in my state, I have to give the money to the police for 60 days. If the owner fails to claim it, it legally becomes mine, and I have to pay income taxes on it. That'll make a mess of my tax filings for the year (suddenly I don't qualify for Roth IRA, for example) but I don't place myself in any legal danger.
It's a boring answer, but I'd much rather have a boring $440,000 than an exciting $750,000 and a constant threat looming over me.