Zizly Needs Advice: How to get rid of soap scum?

Ok, so my husband and I bought a home last month, and luckily, we've only had to change cosmetic stuff around the house. Choosing paint colors and transforming the color of a room is where I thrive. I love to refurbish old furniture and items, so the decor department is taken care of too. But...there's one thing I haven't been able to tackle. SOAP SCUM.

Seriously, I've bought several different cleaners and NOTHING works. After letting stuff sit for hours, and scrubbing until my elbows hurt, the scum remains. I would LOVE to just tear the whole thing down, but that's not quite in the budget at the moment. So, that's where you come in. Is there any product that you swear by? Maybe a spinning brush? Laser beam thingamajig that burns it off but doesn't damage the glass? I need help. I'm getting desperate.

Maybe you even have a home remedy that you need to tell the world about, I want to hear about it! Give me your ideas in the form below. I'll be posting a video to show you the damage and HOPEFULLY the transformation. Thank you in advance!