Looking for a phono stage with pleasing coloration

Two options. One cheap, the other still within your budget. Cheap one, Audio Research PH3SE. Had one well over 20 years, has all the qualities you want. Specifically the warm woody tone with good extension. The warm woody tone is very slight. Did not even think it was there at all until going to my current Herron which is in every way far superior, but unsuitable for you since you ruled out superior in favor of colored. A little over budget anyway.  

Within budget, Decware ZP3 which even with their SUT is still well within your budget. https://www.decware.com/newsite/ZP3.htm This should give you everything you want, and then some. oldhvymec has one on order so check back in a few he will probably have some good news to report.

The Decware looks beautiful but the gain is too low. The gain on the Adagio is 64db but I wish it was a little higher. I like to run my poweramp slightly attenuated and drive more of the gain from my preamp (for whatever reason I find my system sounds better that way); preamp only has about 10db of gain so I'm already running it pretty hard hard. I know I'm going to sound picky but gear looks also matter to me and I just don't dig the industrial aesthetic of Audio Research gear. I also would like readily accessible controls on my phono stage (so not a fan of opening cases to tool around with dip switches). Price point wise, I could push myself to $4K for the right product. Thanks. 

I missed your comment regarding SUT for the Decware. I will look into this. Thanks.

I have the Soundsmith Paua II into a Simaudio LP5.3 with the external power supply, and as Soundsmith and others report the Paua II is a bit lush and sultry.  I run the loading at 1000 ohms for a bit more high frequency detail.  

How is your cartridge setup -  the tonearm  TA-RB880-RETAIL-UNI.pdf (rega.co.uk)  does not show the ability to alter the vertical tracking angle (VTA) which for a high end cartridge such as the Paua II can be critical to get the best results.  Can you set VTA?  Viewing the telescoping aluminum cantilever which has a flat spot where the stylus is inserted, is that flat spot level or tilted with the record?  Each position will yield a slightly different sound quality.  Tilted too far fwd "will tend to have good stage width but the strings will sound unnatural, edgy and irritating.".  Tilted too far back "the sound will be slightly muffled, with a lack of high frequencies and air around the instruments."    Sedrik Harris: Setting Up Cartridge VTA (enjoythemusic.com) .  Others on this forum can fill-in with more details and there are many articles on the web on VTA. 

What loading do you use with Travish?  The maximum is indicated as 500 ohm which would be the 'normal' minimum (470-ohms actually); lower would cause some high frequency roll-off.  Have you tried running at 400-ohms?  Also, have you tried tube rolling?  The Travish manual  Microsoft Word - adagio_owners_manual_rel6.docx (shopify.com) implies its using new current available tubes - not New Old Stock (NOS).  Some NOS tube(s) could make a huge difference.  Check with Travish to see what tube or tubes will have the most musical impact; and then consider some NOS for that or those tubes.  

Just some thoughts.  Good luck.

Dealer came to my house and professionally installed Soundsmith; he also used shims to adjust VTA. I have always run cartridge at 400 ohms (and going up to 500 doesn't make much of a difference). I think the setup and installation is well done. I'm also already running NOS tubes (GE 12x7 and Siemens 12au7). I used to find tube rolling fun but I'm a bit over it now; there's just too much variability with tubes.