Selamectin, which is what is in Revolution, is the same thing as Ivermectin. While they are different medications, they do the exact same job. You're correct that ivermectin injections aren't the best option. They're expensive [generally], don't always work, and can cause a reaction at the injection site. Overall, not worth the hassle. Using Revolution, or using Ivermectin orally, is preferred. You already tried the Revolution, and didn't get any results, so I honestly still don't think it's parasitic. Also, for future reference, don't let them do a skin scraping, no matter who you wind up going to see. It's stressful for the rat, and 99% of the time it comes back with a false negative anyhow.
Baytril is really the medication of choice for URI's. Doxy is okay, but it's not as strong as Baytril, and is most often used along with Baytril. Sometimes the problem does clear up with just Doxy, but if this doesn't clear it up try and ask for Baytril.
I'm afraid I don't know Australia all that well, but it may help for you to make a new post, making sure to mention your location, and see if anyone else may now of a vet nearby to you.