Hey all, been having an issue with my beloved 91 300E

It happened when I was driving to work, everything was normal and had no warning of an issue when suddenly at a stop light, on a busy street she died out completely. I tried restarting and she would crank and try to start up but wouldn't. I had her towed home and assessed the situation the next day. The longer she sat, the longer she would run. If you hold the RPM's up she could run forever, but when shes at idle, she'll start to miss and then conk out.

I had her towed to a indy and they told me it was the fuel pump and wanted 700$ to fix. But it really doesn't feel like a fuel pump issue to me. The pumps aren't making any wonky noise and I don't have a loss of power other than just idle. Today I put fuel system cleaner and fresh gas, drove her around the streets for 45 minutes and had a little "bumps" at idle here and there. But I made a sudden stop and she died out. So i tested it, every time I brake hard or suddenly she dies out I feel like it's something electrical... Can anyone give me any leads of where to start? Thanks!

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2007 BMW 328XI