I haven't spent enough time with the P-200 to know, but for those that have seem to indicate it's sound isn't necessarily related to the P-1, so I wouldn't automatically associate.
The Pico is a pretty good source, but as it doesn't err on the warm side, if you replace it you can choose where to add your warmth. As the CD3K is so easy to power I wonder if source might be your best bet. The CD3K hasn't been my main cans for awhile so I haven't pushed them. In fact their lack of requirements are where they've found use for me (Pico DAC/amp or even straight from the iPhone).
Back when Sony was making them it seemed like everyone was powering them with Singlepowers. Probably some nice tube combos with the PPX, MPX3, Extreme, etc. Although I never had the WA6 and CD3K the same time, I could see the Woo with the right rectifier moving the midrange nicely forward and keeping the top from being too bright (why I sold my first two pairs). And I suspect HeadphoneAddict may be on to something with the Cavalli. Although I wouldn't call it warm, and it's obviously not a tube choice, I wonder about the FET-A too, as it would seem to have a complimentary signature. Voltron may be able to pipe in on that as he has/had both.