Budget single disc player-under $600

Jolida JD-100 is the player to have in that price range.

Where can it be found, new, at that price?

There is a JD-100 on Audiogon for $560. Tube rolling yields excellent results with this player.
The advantage of buying used equipment on Audiogon is you get more for your money and if you don't like it you can usually sell it for what you paid for it.
Or you can buy one of the inferior CD players you mentioned above.

The Music Hall is better than the Jolida IMHO. I own both. The Jolida does respond well to tube rolling should you decide to go that way. The best tube I found were original NOS CV military type issue 12AX7 Mullards. Before the tube roll it sounded dreadfully sluggish and muddy believe it or not.

What sounds good is a matter of personal preference and past experience. I'm having qualms about the Music Hall. Just read that the Phillips transport in a Shanling CDP (MH and Shanling
are cousins) is dreadfully slow, and there is talk of upgrading, as if it's not quite right out of the box.