For Tubes, LTA ( Linear Tube Audio) make great integrated units and great tube gear. Aric Audio is a Boutique custom Tube gear house that if you search this site you’ll find a lot of love for. Primaluna (I had the Evo400 integrated for several years) is great option but not in the same league as LTA, Aric is also likely a step up based on the custom, quality parts but Primaluna is really easy to use. Audio Hungry and Cary previously mentioned make fine integrated units as well.
Have you thought about a hybrid design? Can offer the best of both worlds. Also don’t sleep on SS integrated amps with the sound signature you are looking for. I was lucky enough to compare SS and Tube gear. I found some SS gear to be more “tube like” than Tube gear. Krell makes a great integrated 300i, you’d likely be hard pressed to find an integrated that matched your desired sound signature description better but has the benefit of SS control, grunt as well. Krell, Pass, Coda and other class A amp integrated’s likely worth a look.
Good Luck.