Fun! The first thing I would do if you have not already, is not consider the CSP3 as a preamp, but instead as a sound shaper. It has such a wide range of voltage output, you can do a lot to tune your overall sound with just the individual tube pots and the CSP3 gain.

I might suggest starting by setting the front right/left pots at 7, and the back ones at 8. Then, set the Rachel attenuator at whatever level you are used to for a satisfying volume for your room and tastes, and bring the CSP3 attenuator up to where it sounds about as loud as you were used to with just the Rachel. Then try "riding the gains" between the CSP3 and SE34 while keeping close to the same volume, to hear how the CSP3 voltage (and all the rest of it) adjusts the sound, when increasing CSP3 voltage, emboldening your sound, and reducing it in the blend likely opening and leaning the sound. This can be really useful for tuning to different recordings.

Toward your end of bringing up bass some... for example...if you liked your amp at half volume, maybe start setting it there without music, and the CSP3 turned down. Then with music, bring the CSP3 master gain up to fit that volume you liked in your room... Then, to amp up the signal, keeping the volume as close as possible to the same, turn the CSP3 up while riding the Rachel gain down at the same time.

This will give a good sense of how the increased voltage of the CSP3 can embolden the CSP3 and SE34 sound qualities, likely including bass, weight, lucidity, dynamics, space, etc, while introducing the fun of using the CSP3 as a sound refinement tool rather than a great sounding volume device.

I was originally running three 6N1P Decware red tipped tubes in my fully modified CSP2+ and enjoyed the sound.  Since I run a ZRock2 before the CSP, I am able correct the bass output. But I do know what you are saying about the bass being a bit thin when my ZRock is at unity gain.  I would say the bass is not as punchy with less authority.

Anyway…I have recently switched the two rear tubes with some NOS 6SN7 RCA VT smoked glass tubes.  As Will described the CSP as a sound shaper…I would say that these tubes make the bass present itself as warmer, holographic, with more authority.  It’s not slow nor is it syrupy..it gives female vocals a more natural sound. That’s the good news.  Now the bad…those tubes are not cheap and you need converter bases for them.  And to top that off..the tube socket screws prevent the base converters from fully seating….so you may also need socket savers to help the converter bases clear the screws.  Does that make sense?  Hers a pic to give you a better visual.  Hope this helps.