I don't get a thickened sound with the CSP3 but all the tubes are chosen to reveal "transparency" and avoid density that is thick or dark. Also, my cables are not particularly warm, though not cool either...I choose them for "transparency," "accuracy," and "musicality." I seem to start with balance and lucidity, and then warm it up a little if needed, but only with tubes that do little or no masking. It is interesting how much the "foundation" effects the choices and results. I use the same basic method with the Torii also...open, spacious, but with balance, body and a little warmth.
I have liked the E288CC in the CSP3 before, but from my usual open/spacious foundation, it is so open, dynamic and powerful, I usually need to compensate with some warmth and calming it down a little elsewhere, so I can see why a 5Y3GT came back in with your experiments.
I have one pair labelled Valvo E288CC that are Siemens made. The maker is clear on this tube with the date code stamped on an internal shield. I have another with a simple red E288CC and nothing else, that is supposed to be Siemens made also and does look almost exactly the same except the stamped shield, so I am guessing it is Siemens but a different vintage... I thought I remembered a Phillips labelled pair that also looked the same. I can't find that pair though. Maybe I hid it in the workshop system somewhere, or I may be making that up#$%^&*().... Anyway I wonder if Siemens made most of them or if those are just more available.
I used an American Amperex 7308 in the input of the CSP3 for quite a while with either open PCC88s...or Mullard made, Phillips labelled E188CCs, Phillips labelled E88CC SQs (also Mullard), or similarly articulate and balanced tubes for outputs. Here, all of these are open but friendly. I liked the American Amperex, with great midrange clarity and texture, bass response, and nice "warmth" that does not cause spaciousness degradation in the right company...But finally it is a little veiled in micro information for me...mostly on top, so I don't use it anymore.
Also, in this foundation, an early RCA 5Y3GT always sounds good to me at first, but finally a little unnatural...a little restrained and held back, but I have not tried it with the big E288CCs!
The tubes staying in the CSP3 lately here are a 60's Phillips PCC88 in front, a pair of early 60's Valvo E88CC (similarly articulate and spacious to the E2s, but mellower) and a warm but revealing Fivre GZ32 for a rectifier.
It is fun to watch things shift and change and to notice a system develop, finally perhaps resulting in similar qualities but from different approaches...everything based on everything else.
It has been a little surprising to me to see you shifting toward more open tubes. Makes sense with your front end change, noise work, and cable changes. I also wonder if your Austin room may have been biased a little bright and away from warmth/bass comparatively. It is all fun!