How can I persuade developers on my team to embrace "You build it, you run it"?
I think the easiest way is to change their performance goals so they are based off reliability as well as delivering code. Sell it as the company cannot succeed without both so why should the developers only be measured on one? The best way for them then to meet their performance goals is to be involved in operations.

Ultimately you need to convince them this is the best way for the company to succeed and therefore for them to succeed. That's hard and you can't expect them to be onboard from the start. They need to be sold on the value too.