Thank you go all of you who have responded to my questions - it's been a tremendous help. I wanted to provide an update and, perhaps, ask one more question.
I tried a different cartridge (Rega Super Elys) that I picked up here on AudiogoN for a reasonable price - just to rule out any issues with my cartridge. While it sounded "different", it certainly wasn't better and most of my issues persisted. I took that to be good news.
Next, I tried another "budget" phone preamp (a Schiit Mani, also picked up here on AudiogoN), to rule out any issues with my iFi Zen Phono. I figured that if I bought stuff cheap enough, there was little to no risk and the troubleshooting could continue without spending needless money.
In the meantime, I followed all of your advice and walked through the setup process of my turntable again. I'm not sure if I heard any improvement, but it helped me feel confident that I had done things properly.
All of this lead me to the conclusion (as many of you already pointed out), that I needed a "real" phono preamp - something more in keeping with the quality of the rest of my system. Against my better judgement, I got on eBay and bid (and "won") a Lehmann Audio Black Cube SE. Unfortunately, there was something loose rattling around inside the external power supply, so I didn't even risk trying it out and promptly requested a return authorization. Next, I purchased a Dynavector P-75 Mk3 for a very good price and was optimistic that it would be "the one". Sadly, I experienced a terrible ground loop that I absolutely could not eliminate, leading me to conclude that there was an issue with the unit itself. The seller hadn't used it in a few years, so couldn't rule out that there was a problem. He kindly refunded the purchase and I sent it back to him.
Finally....I purchased a Musical Fidelity M1 ViNL phono preamp from a very nice seller here on AudiogoN which arrived yesterday. I promptly unpacked it, marveling at how substantial and beautiful it is. I hooked it up directly between my turntable and control amplifier (integrated) and put on the first record. It was a revelation!! This thing is so quiet and dynamic, it's amazing! I have lots more listening to do, but I can finally hear where vinyl is "as good as" a nice digital front end and clearly has the potential to beat it.
All of which leads me to one more question, if you will indulge me. As you may recall, my cartridge is a Clearaudio Virtuoso which is a ~$1,000 moving magnet cartridge. I would like to try moving coil but am wondering whether something "affordable" like the Denon DL-103 could possibly equal or better the Clearaudio, or is that unrealistic? If so, what would I need to budget for something that would clearly surpass the Clearaudio - and do you have any specific recommendations? I like to keep it under $1,500 if at all possible.
Again - I want to thank you all for your thoughtful replies and assistance. It's been a struggle and, at times, incredibly frustrating, but I feel like I'm seeing some light at the end of the tunnel and am looking forward to buying more records and actually enjoying my investment.