There is a hardware device, called a compressor that would solve the problem. Basically it reduces the loudest parts of audio on a gradual curve, which allows you turn up the overall volume.

Affordable ones range $100-$250, which should get the job done. Personally, I wouldn’t go either direction out of that range, more expensive ones will be overkill and cheap ones could sound bad or lack the controls to set it up right)

If you can get analog audio out of the TV in to a speaker/sound bar, it’s easy to setup.

So with a cheaper sound bar and a compressor, you could accomplish this for about $250-$400 depending on how much money you can to throw at the problem,