Silver Amumu main having trouble dealing with fed vaynes

Hey guys!

I'm a jungle main, and I love amumu. He's basically the only champ I play, and honestly one of my favorite video game characters ever. I know he's not "in-meta" right now but I really have fun playing him. I'm silver 1 right now with a 60% win rate, maxed out at gold 3 this season so far, then hit a bit of a slump. Just didn't have time to play for a while because of school, and just now getting back into it. I'm on the rise, hopefully I'll be able to hit gold again. Maybe even platinum.

One champion I have had trouble with since I can remember is vayne. Especially if she gets fed. The issues that I have with her is that I really have a hard time sticking to her or getting her in my ultimate because she simply condemns me away or tumbles or both. The other problem is that, while I'm tanky enough to sustain damage from almost any champion in the game, it seems like vayne just melts me like a hot knife through butter.

Other than just banning her every game, which I've strongly considered, are there any strategies that you can recommend for dealing with a hyper-fed vayne as amumu? Any itemization choices or strategies that might help me deal with this? Are there any ADC champions that combo well with amumu specifically to handle a vayne (My duo buddy always plays adc, usually tristana).

I could obviously just ban her, but I'd rather learn to play against her and win. Any and all suggestions would be helpful!