Major upgrade from Rega Apollo: Which one?

So someone told you that an outboard DAC would provide little or no improvement, and you are prepared to just believe them? Why? I disagree. Just for starters, why not check out an Eastern Electric or a entry level used Audio Note. I think you might change your mind.

You were given very poor information.

I went from a Rega Saturn to a Sony 5400 and was very pleased. I recently sold the Sony to finance a computer/DAC project, but I *really* miss the Sony and may end up buying another one. All of that said, as always, you would have to hear it in your own system to determine if the changes are "major," or to find out if it achieves your goals of improving bass, eliminating midrange glare, and getting smoother, cleaner highs. (For whatever it's worth, I never found the Rega Saturn to have any of the problems you mentioned--perhaps some other part of your set up is contributing to these issues?)

I own a Rega Apollo, and I added an outboard DAC (Hegel HD11). It made a big positive difference. More open sound, more precise, more details. I have since moved to computer audio, but adding the DAC was not even subtle.

I've owned the Rega Apollo and the SONY 5400ES.
The Rega paired with a BAT VK-300SE integrated was the most musically satisfying system I've owned (Thiel 1.6 speakers).
The Sony through an Onkyo SR876 HT receiver was kind of generic sounding.