I definitely agree that adding another piece of equipment to mask the problem makes no sense, as it would be better to just eliminate the source of harshness, although it may be a more difficult task. Also, changing to a tube preamp will definitely sound different, however, if the preamp is not the problem, it may just mask the harshness like a tube buffer. I have to ask at what point did this harshness begin? Can you recall an equipment change when it started, or has it always been there? If it resulted from a change, then focus your efforts there. If its always been there, then I would start with the source components. Have you tried a CD player only, rather than transport and DAC? Is your digital cable extremely short or at least 1.5 meters in length to help minimize jitter? I helped a friend audition many digital cables in varying lengths and types. Results ranged from very smooth and laid back to bright, harsh, and forward. I have also tried different CD players (SS and tube) in my system, and found that some tubes can even sound harsh.
Spend a few tens-of thousands to fix it. Then discover it still sucks.
Anyone that throws expensive components and cables at a system to solve a problem is foolish, and should just get out of the hobby. Also, solving the problem correctly allows for greater benefit in future upgrades.