I personally do not take my rabbit's health into my own hands despite all I read; I see a vet first and then verify what they say with my own research. I know that not everyone can do the appropriate research and make an informed decision. My profession is as a research scientist in biomedical areas so I have the background to read scientific articles and texts thoroughly and make appropriate decisions based on them. Veterinarians are trained to translate the science into practice. That is why the word of a veterinarian, if they are staying up-to-date and were trained well, trumps all. I also do not find the scientific evidence or rationale for the "drown the parasites in oil" treatment to be very compelling. There is a lot of anecdotal evidence, but that is all.
In this particular case, it sounds like the rabbit may have another issue going on. It is quite common for rabbits to have fungal or bacterial infections in the mouth and genital area. One obvious example would be rabbit syphillis, and the broken skin caused by the mange mites could have also opened up the possibility of an active, opportunistic infection by one of the species of yeast and/or bacteria that are commonly found on the skin of a healthy rabbit. I would encourage another skin scraping, with a focus instead looking for microscopic pathogens instead of just the larger multicellular parasites.