My traditional Japanese futon got mold - is there any way to get it out or should I just toss it?

My brother bought me an awesome futon bed with a tatami platform and a traditional cotton futon. I didn't get a cover, because sheets. At the futon shop they didn't mention anything special about how to care for it, and it didn't come with instructions, so I just used it like a regular mattress - slept on it, sweat on it, made my bed in the morning and that was that. Fast forward just a month or so and I discover black mold growing on the underside as I'm flipping the futon.

I did all the usual stuff like taking it outside and beating it, spraying it with white vinegar and water mixture, leaving it to dry in the sun. The surface mold is gone but I can see underneath the black spots are still there. So for the past month I've been sleeping on a few thin blankets spread on top of the tatami. It's fine for me, I like hard surfaces, but my girlfriend is not a fan, and I've got this moldy futon taking up space in the corner.

Some websites say there's nothing to be done if mold gets in the futon, just toss it. Others say you can put it the washer, and there is a laundromat down the way that has a huge washer and dryer, it looks like a portal to another world. Should I spend $20 in quarters and give it a try? Is it worth it? Can it be dry cleaned?

Thanks for any suggestions. I feel bad tossing it, I just got it a few months ago, but I guess I will if I have to.