Warm Tube Amp(s) to Tame Hyper-Accurate Speakers?

What about the source? 

That is a warm rig going into speakers that are not known for being bright.  I would need to dig into it, sometimes the wrong impedance curve on a speaker can make a tweeter sound hot when paired with a tube amp.  You might find switching to a neutral SS amp. Naim, AVM, AGD come to mind for me.  You should be able to borrow or buy on an amp on a return policy to test this.  

how is your room?  Damping matters and if the room is underdamped it could be creating this issue.   
 

Finally, If you are looking for a more “English” sound maybe Harbeth or Wilson Benesch will solve the issue.  You ought to be able to find a used pair of used 40.2s or the P2.0s in a similar price range.  

Without changing speakers, there are a few things you could try.  Some previously mentioned:

• felt tweeter rings
• Mullard CV4004 preamp tubes are fairly warm
• different speaker wires/
• different cables
• room treatment
• scrutinize your sources

Have you tried playing with inverse toe in? In other words put the speakers to point at the side walls at your listening position, then gradually move towards the paralell position until you have no blind spot in the middle of the soundstage. (You may need some Isolation on the first reflection point on the sidewalls to make it work. Changing the amp seems to me completely the wrong approach. Alternatively putting a large shaggy carpet in front of your listening position may achieve similar gains.Sometimes putting isolation boards on the ceiling halfway from the listening position also works

Have you tried playing with inverse toe in? In other words put the speakers to point at the side walls at your listening position, then gradually move towards the paralell position until you have no blind spot in the middle of the soundstage.

Side walls are a known source of harshness due to causing early reflections. So I see this as bad advice. Instead, toe in the speakers, possibly to the point that they cross in front of the listening position. Side wall reflections must be controlled else they are well-known to cause harshness. If the tweeter has a wide dispersion characteristic, this can make setup tricky.