Mike, so often, it's the loudspeakers that are the culprit in an amplifier coming across as hard. However, that's an argument for another time and place, so let's continue to focus on the amplifier.
In today's world, there are scant few examples of true tetrode/pentode amplification. You have to look long and hard to find them. What makes things all the more confusing is so many amps labeled "pentode" are actually ultralinear. As I said, UL rules the day, and has since the 1950s.
That said, given the case you laid out in initiating this thread, I think you would would find more happiness with UL than pentode operation, the latter sounds more forward, open, and to use your term, hard. Pentode would steer you more in the direction you're trying to get away from. So, I think UL might be getting a bad rap if you think it sounds hard.
Here are three characteristics that can "soften" an amplifier:
1) Triode operation
2) Cathode (or self), as opposed to fixed, bias. To put this in a more understandable way, though it doesn't hold up all the time, look for an amp where the tubes are "plug and play", and need no adjustment of bias on the part of the user. The label "fixed bias" is counter-intuitive to most folks
3) Tube rectification
I wouldn't exclude a product based on having having only one or two of these features, as I can name some amps with only one of these three that sound quite warm and lush. But again, generally, these three take things toward where you mentioned wanting to end up.
