Alright Grasshopper, I'll throw my 2 cents into this discussion.
Stereophile defines neutral as being "free from coloration". I personally don't like using the term and in the context you seem to be using the term it seems even moreso out of place in describing the Rega Planet 2k. The Rega is a very nice player that tries to capture a more analog sound, it leans to a warmer, fuller sound that seemed to me to be a bit rolled off at the freq. extremes and sacrificed detail and air to achieve a more musical sound which goes against the definition of neutral as stated above.
Finding a CD player with a decent headphone output is a tough assignment. I agree with Teerawit that the MiniMax is the only one I know of that has a decent headamp but I don't agree with his assessment that because it includes a decent headamp that it's CD performance is somehow compromised compared to other players in it's price range. In fact in many instances the MiniMax compared favorably with machines costing much more and in my opinion is a much better player in both sound and build quality than a Rega Planet 2K which a few months back was selling for the same price as the MiniMax new. The MiniMax is now selling for $1100 and is maybe not quite the deal it once was and there are some other players like the Eastsound that have emerged at a lower price point that may be better on a purely sonic level but it still has the all-in-one, compact, tubed CD player market cornered. But neither of those players are in your price range so it's a moot point anyway.
So what worthwhile players are out there in your price range of $400? Unfortunately it doesn't seem like a whole lot. The NAD 521BEE and 542 are two choices that are usually recommended but I haven't heard either. The Cambridge Audio Azur 640C could be a contender as well. From my recollection it's faster, more balanced but a bit brighter and leaner than the Rega.
Have you considered a separate DAC solution? Probably some of the best deals in audio right now are the lower cost non-oversampling DAC's especially the ones coming out of Asia. I prefer my MHDT Labs Dialogue II to anything I've owned and it only cost me $225 including shipping. MHDT Labs hasn't had any DAC's on eBay for a few days but there are others on the market like the
Moodlab DAC and the
DAC-AH from DIYCLUB.biz which goes for a mere $135 + shipping. Add on a cheap DVD player or CD player as a transport and Blue Jeans Belden 1694a coaxial cable for a really kick ass cheap source. Of course add on a better transport and the sound will only get better. The only downside is non-oversampling DAC's can only take a standard 44.1 Khz redbook CD signal so no SACD or DVD-A.
