Hi OP,
Over the last 4 years or so I have been on a 2 channel journey that has seen quite a few upgrades, tweaks. On that journey I have had the Primaluna EVO 400 integrated, the Coda CSIB integrated, Krell’s latest Integrated along with Parasound A21 and Krell 300xd duo stereo amps with Krell Illusions ii or Zesto Leto Pre (Tubes). I also used the Coda as a Pre for a spell. I was looking for the control, balanced and drive of SS with some of the warmth and 3 dimensional magic of Tubes. For my tastes, I found SS amps that had some warmth, magic was my preference. I also found that I preferred the Coda Pre which is SS over any other Pre I had in the mix. The amp champ hands down was the Krell 300xd - bested the Krell Integrated and the Coda Integrated.
I’d look at used Amps, likely Class A, known for a touch of warmth, tube like qualities that can drive speakers at least down to 4 ohms. This gives you flexibility on speaker selection, will work with almost any speaker. Used Krell amps, Coda #8, Parasound for the $$ offers some great amps. Schitt Freya Plus is a steal, bargain on a pre that offers tubes and SS. I’d go with that Combo or I’d by a Coda CSIB, used but latest version and version 1, add a power amp down the road using the CSIB as a Pre. There are also some boutique Tube brands that could get you to a great Tube experience, another route. Or, as previously suggested, upgrade your speakers to speakers you plan to live with for quite awhile and the build around your speakers, if you don’t have the speakers right nothing you do after will transform your system or speakers to what you are looking for. An analogy would be you can’t exercise your way out of a bad diet. Same with speakers. If you love the speakers you have, you are 75 % to where you want to be.
If it was me, I would search for used Cosa # 8 or used Krell older amp or latest XD amp used, buy the Schitt Freya and potentially upgrade the Pre which you can sell for a minimum loss if you upgrade. Also pay close attention to the “House Sound” of the pieces of gear and brands you buy. Benchmark is all about zero coloration, distortion, the make great products at a high value but based on your referenced lean toward tubes, not a great fit for what you have described as your house sound. Some Tube gear leans more toward SS, PrimaLuna is one brand that does while some SS leans toward a Tube sound or warmth, think Pass, McIntosh, Parasound and the older or newer Krell gear. Some Tube Brands chase bridging the short comings of tubes vs SS and some SS brands do the reverse.
Welcome to the forum and good luck!