Folks here were very helpful in navigating how this process worked and in figuring out if it was even possible for my wife and I. We were able to manage it, from start to finish, in just under three weeks. Here was the timeline:
July 9th: I (US citizen) got a job offer.
July 10th: I sent the formal request for DCF to the Vienna embassy.
July 14th: After a bit of back and forth (the offer needed to be on a formal letterhead), the embassy approved the request. We could come in any Tuesday or Thursday (surprisingly, no appointment needed).
July 22nd: We both (me and my wife) came in for the formal I-130 petition. The consular officer interviewed both of us about our relationship, and they really liked the short booklet we had prepared with pictures/the story of our relationship (HIGHLY recommend you bring this! It won't be formally requested). We were approved immediately. They even asked us when we'd want it by; we asked for mid-August, which they said was no problem.
Edit: July 28th: Medical examination (forgot to add this). The consulate had a specific doctor she needed to see, who was pretty quick.
July 29th: My wife's interview, when the I-864 was filed (she had previously, after I-130 was complete, done the DS-260 online). This required some last-minute maneuvering (my parents graciously agreed to I-864A and we hurriedly got everything in order for that). Likewise, we had police reports from any place she had lived over the age of 16 for more. Do NOT wait on these. If you think a job offer might be coming, get them anyway (good to have on hand in case you unexpectedly need them). The countries we needed would have been quick anyway, but some take a very, very long time. There was unfortunately one hiccup (related to my parents' taxes; just did not have the correct form), but they said we could just email it to them. My wife self-translated her birth certificate, which was fine for them.
July 29th (part two): By a literal random chance, my parents found the correct form an hour after my wife left the consulate. We emailed it to them promptly.
July 30th: We sent another followup. They responded quickly, saying they'd get back to us soon.
July 31st: Green card approved! They got back to us, approved the form, and said my wife could come in whenever to get the initial visa thing (the one they print in the passport).
August 1st: My wife handed in her passport, and shortly after got an email saying to pick it up Monday (August 4th).
Overall the consulate was incredibly friendly, professional, and efficient. If you feel like you're staring down a DCF barrel, stay calm and (if you think DCF may be a feasible possibility in the future), have the key documents ready ahead of time. Likewise, know your addresses DS-260 wants to know everywhere you've lived the last ten years. We did not necessarily and many of the pieces came together seemingly by chance. Good luck - and thanks to you all!