No, this isn't possible.
I understand what you want. But, the product you own is not designed to do this.
No, you can't modify things to make this work.
No, there is no workaround.
Bass shakers are designed to be connected to the LFE (subwoofer) output of a AV receiver. If your soundbar had a LFE output on it that could connect to any of the thousands of standard subwoofers on the market, you could make this work. But, it doesn't. So, you can't.
Speaker bars are meant to be a quick, cheap, and dirty way to improve upon the audio built into a television. They are never 'great', or nearly as powerful as advertised. But, they are a real improvement over the TV speakers. But, that's all they are. They aren't AV receivers, and they are a midway point between terrible audio and quality audio. Okay audio. Acceptable audio. Which is FINE! There's nothing wrong with improving and meeting a budget, but you gotta realize that these things are built to sell in quantities, and performance and connectivity are just there to hit the most people they can for the least amount of money possible. Which means, no added connectivity that most people will never use.