Manley Chinook with (very) low output MC ZYX?

should work fine. I have exact same phono pre.

also have the ART-9 and lower output LOMC carts; Benz LPS, and Madrigal Carnegie One which are both around 0.2mv output levels.
You will need to move the gain switches up to the highest setting.

Have been using RCA 6922s and Holland Bugle Boy 6DJ8s in mine.

If you want to drop the noise floor further, replace the TL082 devices with  sparkos labs discrete devices; SS3602 parts... No soldering required, a plug in replacement

https://sparkoslabs.com/
good luck.

To answer first question:

I am using 60dB of gain on the Chinook for my 0.5mV output ART9.  On my Bryston BP25 / 4BSST amp setup, I listen between 8:00-11:00 on the preamp.

I have the first version of the Upscale Audio SE.  So in only has the 45dB, and 60dB gain settings.  I could send it in to Manley to have the additional two added.  Maybe 55dB, and 65dB.  Is this probably needed for a 0.25mV cart?

As for the Sparkos labs devices; it seems they make discrete opamps.  Looking inside the Chinook, I see three TL082 opamps; one per channel, and one on the PSU side, are you talking about all three?  Are the ones on the channel side used for input?  A review I had read stated they were not in the signal path, but rather used to bias the JFETs.  I have seen a similar idea in Kevin Gilmore's designs.  Did you notice a significant difference?

 I have an opportunity to get a good deal on a ZYX R1000 AIRY 3X/SB (0.24mV).

There is a better model, i remember my upgrade from Airy to 4D, my advise is to look for at least Zyx 4D or Premium 4D  

I own a Steelhead; I use it at 65db setting with an AT ART7, which has about the same output as a low output ZYX. You will have no problem. Moreover, I like my low output ZYX UNIverse a bit more than the ART7. 

The nice thing about the 4BSST is that you can change the input sensitivity to 1 volt.  You will need approximately 72db of gain to drive your amplifier to full gain using the 1volt input setting.  The Manley can provide 60db of gain coupled with the Bryston's line level gain of approximately 15db, therefore, you will have a total of 75db of gain available.  You will be fine.