For what it is worth. I got the 300B bug a few years ago. After hearing about them for so long. I also had a pretty good headphone system. I had the bright idea that since 300B systems tend to be lower power and that it would be a great match would be on my headphone system. Then if I liked what I heard I could see where to go from there. Wow, that worked really well.
My headphone system got two enormous boosts in sound quality all at once, from the realism of the 300B and a huge boost in power / current. I now listen to my headphone system all the time. It has jumped an order of magnitude in satisfying sound quality. It also, started a complete revamping of my main system to tubes… but not 300B… higher powered ones. So I get the best of both worlds in my main system.
The tube headphone amp I bought was a Woo WA5. It can be a tube headphone amp or an integrated amp powering speakers. Woo amps are simply fantastic and this is my third. I highly recommend it. You might consider a more tangential strategy, it worked for me anyway.