Unlike the old days when solid state amps sounded grainy or harsh, modern amps are quite smooth and not at all harsh. There are brands, like Accuphase and Rowland that are also on the warmish side. But, what good tube amps deliver (meaning not all tube amps) is great dynamics at low volume (micro dynamics) and lively sound when playing at modest volumes (one tends to want to crank up solid state systems to get the juices flowing), a sound that grabs your attention so you want to listen more carefully instead of allowing your attention to wander, a sound that seems to envelop you more than solid state, and a more relaxed (not as edgy) sound while still being lively.
The downside to tubes has to do with compatibility with speakers, bass control and depth that is not in the same league with solid state gear, inability to peel paint with high volume (unless one buys super power tube amps, many of which sound harsh and brittle), and putting up with some maintenance issues or problems with noise or channel imbalance.
I know that the Synthesis Audio A40 does not meet your criteria, but, if you have a chance, audition that amp to hear what a good, medium-powered tube amp can do. That would be, in my opinion, a very tough to beat benchmark. If you can do without balance connection, listen to what Audio Note Oto or Soro can do. Other brands with, to me, good sound include Allnic, Air Tight, and Weytech. Certain old Cary amps were also good, but their warmer sounding models sound a touch murky and sluggish (still very good at reasonable, used prices).