TV speakers, impossible. A good amp, absolutely. Especially if you happen to have a powerful 7.1 surround amp that comes with high-end wires for that channel separation and frequency range. It's all in the frequency range. DD will accomplish most of the stuff you mentioned in your post, but DTS takes it up a notch.
I have neither! I'm on a hifi amp but an 8-speaker setup, with the mids, satellites and especially woofers cleverly placed to give off bass that you can not only feel but hear as well. The mids and sats also do a great job of letting me hear what the engine and exhaust are doing. I'm literally feeling in my chest and feet what the exhaust is relaying throughout the rev range, thanks to the two woofers. Heavenly feeling. The more you turn up the sound, the better it feels. No distortion or fatigue. Although I have to take it easy on the volume as my room doesn't have the best acoustics, so it can get "echoey". Turning down the decibels on the mids and highs usually counters that.
I will again use FM4 as an example - the samples really bring your sound system alive and you feel the grunt of the engine and exhaust. FM5 took that a step further and cleaned up the sound a lot. In FM6, to truly enjoy that visceral feel you need to turn the sound up more and use the "headphones" setting.
I've contemplated many times upgrading to a good 7.1 surround setup to hear and feel racing games truly as the developer intended, but I'm happy with my setup, and just don't want to be spending anymore time than I already am in front of the TV and Xbox.