I know I'll regret this, but I'll wade in...
My take on it is that if you want to learn how the audio electronics really work in a hands-on way, building a DIY tube preamp from a tested/well-regarded design or from a kit can be a rewarding introduction. Fortunately, a line level preamp has a very easy job to do. A preamp with gain is completely unnecessary in most contemporary systems (as you probably already know), but a low gain tube preamp is a simple thing to design. The chances for success are high.
However, if you're looking to buy a ready-to-use tube preamp for cheap that isn't just a high-distortion effects box, then the chances for success become pretty low. I purchased one of those little 6DJ8 > MOSFET source follower headphone amps and it was
horrifically bad. It audibly distorted into all headphones. It just sounded fatiguing and
awful. I suspect the currently popular 6J1 based preamps are just as bad. (I think amirm measured one and it was indeed very bad.) A lot of these Chinese ebay tube audio things are poorly designed. I'd say stay away from those unless you already know how to modify something like that to get decent performance.
On the other hand, there is a certain attractiveness to the old 'romantic' tube sound. I don't think it's better than anything else. These days my system is all solid-state (even the phono preamp), but I used to enjoy that 1960s tube sound back when I was young. There are some "Little Bear" preamps that look at least somewhat competently designed (by vintage vacuum tube standards only, mind you). They look like vintage circuits done well enough to get an idea of what that sounded like -- but I can't guarantee it because I've never heard one. I'm going by the schematics and online descriptions only.
So in the end, I'd look at this as an experiment. If you've never had a piece of tube audio gear and you're curious what that sounds like, then it might be worth it to you to scratch that itch. But as previous posters have said, if you're looking for a particular sound, throwing real 21st century tech at the problem is more likely to give you what you want. I agree that EQing your system for flat response (or a target response)
in the room is a great idea. It could be that the 'harshness' you're trying to fix is a problem with how your speakers interact with the room acoustics.
If you want to get more tube-friendly advice on this, hop over to
diyAudio's tube amplifiers forum.
Best of luck finding what makes you happy.