I've also read so many reviews on $500 to $1,000 integrated amps and they all discuss sound quality & tonal balances. Some amps are warmer than others. Some give better separation and air. Some are U or V shaped. Some..., well you get the point. I'm not an audio engineer, I just trust my ears. I did at one point long ago own much higher end gear (before it all got lost in a flood).
If you just trust your ears, you would have to blind listening tests, otherwise you cannot trust your ears because it has been proven by authoritative audio experts, including Dr. Floyd Toole and Dr. Sean Olive that ears, even perfect ones, are very much affected by the brains that make you hear things that aren't there when you don't know which speakers (let alone amps).
You might have heard that Marantz made theirs to sound warm and with emotion blablabla, so if you prefer warm sound, go get yourself a Marantz amp, and CD if you are thinking in terms of CDs and DAC, or a Marantz integrated amp with build in DAC. If you do that, be sure to read their marketing information so you know what your are supposed to hear, by them obviously, and then you are all set to hear the sonic signature you are expecting.
I enjoy the way my system sounds as it stands now, but the purpose of the original post was just to see if anyone thought that external dacs might offer any improvements over the built in dac of my CD player.
Since you just trust your ears, I am not going to bore you with specs and measurements, so I would suggest you spend a small amount on an external dac that you can easily change the "sound signature" to find out if you can hear what you may be looking for and if not you can return it anyway if you buy from Amazon.
If you search hard enough, you should be able to find such a dac under $500. I have a smsl su-8 that is now hard to find and the su-9n is now selling for $399.
My SU-8 has the following options for different sonic characteristics, you have more than a dozen different setting to try, with a huge number of combination to get the sonic signature you prefer.
By the way, just found one for you at Apos Audio, with a 45-day return window. I have mine for a few years now, I love it, there is no need to spend a ton of money when this $250 thing that is based on the ESS Sabre DAC, the ES9038Q2M (32 bit 768 kHz) can play any file at any resolution and has THD+N spec of 0.0003%
SMSL SU-8 Version 2 DAC (Digital-to-Analog Converter) – Apos Audio
At $250, nothing beats it!