If only there was a name for something with built in amplification, processing, video inputs, video outputs, audio outputs, and volume control....
There is! It is EXACTLY what an AV receiver is.
I know, that's not what you say you want, but that is 100% exactly what you described in your first post.
You don't want a big one, but you want the core functionality of what all AV receivers do. They take video, pass it through to an output, strip the audio off of it. A pre-pro will not have an amplifier in it, a typical receiver will.
I'm not sure what about your $30 purchase didn't work. I use HDMI audio extractors all the time with GREAT success. So, some details of what you plugged it into and where unhappy with may matter. The big thing about HDMI audio extractors is that they do not have a volume control built in. So, you would need a speaker set which had a volume control of some sort. HDMI audio extractors JUST take the audio off the HDMI only device.
None of which is much different than using the RCA outputs that are already built into the TV you own. Which is what they are there for, and what should actually be used.
EDIT: I looked at the manual for your TV and it doesn't look like there are RCA analog outputs on it for audio. There is only a digital audio on RCA (S/PDIF) connection on the back for digital audio. You still will need a pre-pro of some sort with volume, or a set of speakers with integrated remote volume control and a DAC to get stereo audio out of the system. I would use the receiver you have if you want to get decent audio.
