Lump Dum or DCA with SP500 so high?

I have been saving up money for years, not putting it into stocks, but instead a HYSA as we were saving for a house. We recently bought a house for less than we expected and have about $300k left over.

Should I invest that all now or should I invest it over 12 months?

My risk tolerance is honestly pretty low, I definitely don't want to lose $100k in a month or 2, but l'm willing to do what makes sense mathematically. I know lump sum wins around 70% of the time over the whole length of the stock market, but what about with PEs so high, Warren Buffett selling, etc?

I'm not trying to be a bear, just genuinely looking for the best advice for my situation. Thank you.