Your need practically cries out for a 6bq5 based solution. There is a large concenus opinion that the 6bq5 is among the best sounding pentode based tubes available- giving more than a hint of SET magic, combined with reasonable real world power. They do not require a big heavy power supply to drive, and are generally quite moderate in heat disipation. There are many choices available for either a basic stereo amplifier, or a stereo integrated amplifier.
You have received several recomendations for a Luxman N150....this is an excellent choice. I would also suggest a Leben CX300 integrated amplifier. IMHO, Leben designs and aesthetic remind me of a well designed vintange amplifier given a nut and bolt restoration using new high quality parts. Either would be excellent choices for your needs.
You can also look for a vintage amp, and then have it restored. A pair of Fisher 20a mono blocks, or an SA 100 would be ideal for your needs, as would a Fisher X202 integrated amplifier (1st version with 6bq5 tubes). Some believe the best vintage integrated is an Eico HF81. Eico basic amplifier choices include the HF86 stereo amp, and HF14 monoblocks. I have all of the above amplifiers (Eico, Fisher, and Heathkit) and can attest to their sonic excellence.
You mentioned SS as a possible option, with the caveat of tube like sonics. I would suggest investigating SS amplifiers that run in Class A...there will be some heat to consider, but not as much as a tube amp. Sugden A21, Musical Fidelity A1, First Watt SIT4 and several Nelson Pass designs come to mind. All would be excellent choices to investigate.
In all cases, I would recommend purchasing used equipment so you can audition several amplifiers over time, and resell what you do not want, to recover your investment.
Please provide an update regarding your progress.