Just to close the loop on this post: I ended up rolling up my sleeves and decided to become an expert on the CC1101. All I actually ended up with was rolled-up sleeves, but I did gain an appreciation for how complex and complete CC1101 is for sophisticated and robust sub-GHz communications.
Unfortunately, with respect to my particular needs, the CC1101 really just wants to deal with structured data packets, the kind with 2-byte preambles, sync words, and packet length fields. It only marginally tolerates mongrel 433MHz signals of the sort that I'm dealing with: those that come from cheap, primitive protocol 433 & 315 MHz transmitter & receivers. For all its sophistication, the CC1101 essentially tells you that if you aren't going to be receiving well-formed data packets with preambles and sync words, then you'll have to use the tradesmen's entrance, where it simply passes out the same dodgy output as the cheap regenerative receivers, but only after you've cracked the configuration code for the 47+ configuration registers. Trust me, it wasn't worth it.
Long story short: the cheap 433 MHz receiver I started with actually did a better job demodulating my rough-and-ready 433MHz signal than the CC1101, so I've focused on step-wise improvements on cleaning up the demodulation from it. One improvement, for example, was the use of a solid power supply (my new Siglent 3303X-E!)... that seemed to go a long way to cleaning up some issues I was having.
Anyway, there it is for others who, in the fullness of time, come across this thread looking for 433MHz and/or CC1101 keywords: know that unless you're dealing with 433MHz remotes which are using protocols that the CC1101 likes to deal with (i.e. those with preambles and sync words), you should probably stick with using the simple, discrete component regenerative 433MHz receivers for a few dollars on Amazon. But that said, when it comes to designing any new sub-GHz radio data transmission applications, the CC1101 is certainly going to be my go-to device, especially now that I've invested the time to understand its capabilities.