In that price range you may not get the tuby effect you are looking for to mask the harshness or edgyness. I have climbed the tube pre-amp ladder and found entry level pre-amps have their own issues which to me is noise in a variety of forms. While the tube will change the character of the current edgy in a way that you will probably like initially, over time you will recognize the new issues.
I always follow the mantra Garbage in is Garbage out. Consider working on the source of the edgyness.
That said I have had a Schitt Freya and Decware CSP3 which are both in your price range. I found the Freya to be noisy and never found tubes that gave me the tube bloom I was looking for. The Decware on the other hand was not quiet either but in a different way that was much more pleasing. The CSP3 also allows gain-riding which gives a lot of control over the tube coloration, it was fun to play with and allows changing the character of the sound without replacing tubes. The tubes i rolled for the Freya were relatively inexpensive but did not change the character of the sound as much as the Decware. Rolling the Decware's tubes was considerably more expensive but also more rewarding in my system.