New tubes...far more power??

Are you sure the new tubes are not over biased?

+1 Yogi...that was my first thought. If the old set was "worn" then the new set would be noticeably more robust in dynamics.

Hard to say. I've replaced a lot of sets of tubes over the years. Gave up on tube rolling after the first few tries proved its just not worth it. So almost always mine are only replaced either after quite some time (years) or they get noisy, or once in a while flare out. The one time I had an experience like yours the tubes had run a very long time, maybe 5 years, and then the new set seemed quite a bit more dynamic and loud. But not strident. Never had that. Not even close. Why we have tubes in the first place, to avoid this. 

Hard to think of any tube that could legitimately be called strident. But that would seem to be our only option. That you got some bad tubes. What did you have, and what did you replace them with? And strident, what exactly do you mean by that? Not quite as sweet as before? Or grating and hard?

Does your amp have auto-bias? If so, you may have to reset and bias to spec for new tubes. The auto-bias then maintains as needed. Check your manual.