Relationship evidence for an 820/801 isn't about proving you're in a relationship, it's about having de facto evidence, which you don't currently have by the sounds of it.
Apply 300, come on a 462 to wait it out, marry and apply 820/801 at reduced fee. Medicare not available until the 820/801 application but she can get travel insurance in the meantime.
Or visa to Oz (462/601 ETA/600) and decide after coming that she likes it and wants to stay, apply 820/801. Registered relationship or married, you'll still need to meet the stringent evidence requirements or face refusal. Bridging Visa A would be granted but not go into effect until whatever visa she entered on ends.
It all depends on what evidence you have. A de facto visa isn't just about showing your messages on Facebook. The 820/801 route will expect you to have combined your lives as much as a married couple living together would have, and that's not something that can he done overnight.
Good idea to do a consult with an RMA (I recommend those that frequent this forum) and see what choices you actually have based on your relationship and if the 820/801 isn't an option now, a timeframe of when it may be in the future and the type of evidences you can begin to gather in the meantime. Then at least you have a starting point.