What Sonically is the Difference between a $1,500 CD Player and a $10K-$25K One?

There's no difference between a $50 and $5,000 one, except for the fancier box.

One assumes you must have blind tested them, yes?

A good signal processing engineer, if they are truthful, will tell you that all decent modern CD players have little difference in measured signal output characteristics. Modern analysis gear can measure things you could never hear. However, things like dynamic range and other characteristics do vary. I doubt very seriously there is any significant audible difference between $1500 and $25000 players. Build quality, looks, etc, sure. I work in defense and we use A/D -D/A converters, quality amps, etc, all the time. Modern devices are cheap and perform extremely well. I suspect the truth is (and I’ll get flame sprayed) you are paying a huge markup and the cost of low production quantity components, rather than greatly elevated sound quality. I don’t profess to have golden ears, but I can hear differences in some gear readily. But when you get to a certain level of quality (meaning not Target level components) there is precious little difference in electronics. I do not include speakers in this since they are both “instruments” and components and can have unique sound qualities.

What's the difference between a $2 cigar and a $10 cigar?

Exactly $8.

Find a dealer with a satisfaction guaranty and compare the units in your own home and in your own system is my conclusion.. Opinions and recommendations will be all over the map.. There are too many variables in systems and environments, not to mention the audio experience is subjective..

Listening in your system and in your home is the only way I know of to find truth for the customer. Forums quickly turn into "makes no difference and you are waisting money" to "makes the world a better place to be, and my unit was a godsend".. Either way you need to hear for yourself..
Magazines, forums and audio shows can help people find interesting gear to evaluate, but other than that, the opinions on most any topic, are so inconsistent to be useless.. You can read 1000s of responses and end up right where you started without a clue, until its in your home and system. Thats just a humble opinion and you know what they say about opinions... In your home, in your system. Trust your ears. The rest is irrelevant.. The BS marketing and, I can hear better than you do, down to the chocolatey sound of a copper wire is all fine, although almost unless when buying audio.. Only way to sort the BS is with your own ears, in a known system and environment like home. Surely people give honest opinions, I'm just saying that a consensus on a subjective subject is not likely to happen..