My 6922 Tubes Are Too Bright!

I’m wondering if the problem is indeed your CDP and tube selection. With regard to your Amperex, there are many variants and levels of that brand leading up to the PQ. The higher you go, the more refined the top-end.

I have also rolled quite a few NOS 6922/7308/6DJ8 in my DAC. I did not find them bright, but found differences in the bass slam and sweetness of the mids.
    Siemens and Telefunken are tubes that have open, dynamic sonics. Their top-end is extended but smooth, never bright. I would not use many of the new production tubes as a reference since few of them present linear sonics. Possibly try the
JJ/Tesla E88CC recommended by @newbee .

Can you tell us what the rest of your system consists of? Room size, any acoustic treatments?
It may be this CDP does not have the right synergy with one of your components, such as speakers, ICs, or preamp.

The only 6922’s that I have experience with are the Telefunkens that I have in my DAC, and they’re not bright. I bought them NOS from Upscale Audio.

I have rolled a LOT of different NOS 6922's in various amps, pre-amps and DACs over the past 20 years. Stay away from the newer orange label Amperex 6922's, as well as the green label ones. The early 1960s U.S. white labels are less forward sounding and have stronger bass than the comparable Holland versions, and well balanced all around. Prices are not near as high as the Telefunkens, which are wonderful tubes as well, but a bit "cooler" sounding (not as warm). The Tele's are hard to beat for detail and clarity, but the Amperex ones I mentioned come quite close. Mullards are warmer, sweeter, and not edgy in general. 

@ 25105 regarding Voskhod 6n23p tubes. As to their sound in the BHK250 - warm in the sense that the mid range seems to have slightly greater emphasis, lots of "air" around instruments, treble is detailed but definitely not etched, bass isn't fat or bloated. They allow a more relaxed perspective as if you moved back a couple rows in the audience. I've got several sets of 70's and early 80's Voskhods I accumulated in my many years of collecting gear and tubes. FWIW, I did order a couple more sets from an Ebay seller in the Ukraine because the desirable vintages aren't commonly found here in the USA.  I've not received them yet so I can't say what I think of the seller. 
https://www.ebay.com/usr/tubesandsound?_trksid=p2047675.l2559

Go to Upscale Audio website. Good coverage, user reviews, some vids and descriptions of 6922s and variants. Kevin Deal knows tubes. There is a certain synergy with tubes in each individual system. Especially when various components use them.