Took the advice of (some of the people) on this forum and elsewhere, I ended up calling her father yesterday days ago and asking for his blessings to marry his daughter. For those who missed the other topic, I bought the ring two days ago. He was quite surprised by the question, but ultimately he just wanted his daughter to be happy and he knew that I provided that and I'm a good guy, so he gave the thumbs up.
So, last night at around midnight (She's on a weird sleep schedule, she starts working an overnight shift next week) we got done with supper, she went to sit down at her computer. She wasn't paying any attention, so I grabbed the ring out of my bag, did the standard proposal (one knee, will you marry me, etc), and she said yes. Talked to both sets of parents/siblings today and sent the ring away already to get resized, updated our Facebook relationship status, and we're going out to dinner in about 50 minutes.
Busy day, but worth it.