UPDATE: So, I tried a few approaches. Each step lessened the oily film considerably but it still hasn't completely gone away:
1) Vigorous scrubbing with hot water + dish soap.
2) "Deep cleaned" glass using IPA, glass cleaner, clay bar & Griot's Glass Polish.
3) New wiper blades (old ones were getting tired anyway).
4) Gas station squeegee. Luckily, I found a newer station where the squeegees weren't beat to hell and the cleaning solution was actually sudsy!
5) Added P21S Washer Fluid Booster (supposed to help with road film).
I'd say it's 80% improved now. There is still a ghosting effect on the passenger side but overall I could see a lot better the few rainy nights I went for a drive. Going to leave it alone and hope it naturally breaks down over time. It's also getting colder and I don't care to stand around outside (no garage) anymore and dirty up extra microfiber towels messing with the glass.