kd-34xbr960 settings

Every set is different because every picture tube is different.
Calibration requires a learning experience of what the calibration is designed to accomplish with the picture. You can read of "unrealistic" (and the contrary) picture reproduction, and what calibration seeks to overcome.

You can also use it as a work light in torch mode.

I agree with STEVE050 that every set is different.

Did your Avia calibration involve the service menu or just the user's menu? Which viewing mode are you using, Pro, Standard, etc.?

You could search this CRT forum(button upper left) or the SON 960 owners' thread to find out more. For terms like black level, contrast, pic mode, even 'warm', hue, calibration.
In LCDs you'll read terms like 'crush' (multiple contrast/brightness levels revealed as the same level/no differentiation.)

You may not be used to watching a calibrated pic for what it brings. Like most, we're used to 'torch'(vivid) mode.

You can also refer to your Sony manual for a little guidance on pic adjustments, and what they were intended for.
You don't have to like the calibrated settings, but it's nice to know what they are.

You evidently only used the user's menu for your Avia calibration and you likely got it as close as the basic controls, (color and hue, brightness(black level) and picture(white level), allow. IMHO, calibration should be done in Pro mode, neutral.

A color decoder calibration using the service menu usually gets it very close; closer than the user menu alone. There are more parameters that can be adjusted. You can do a lot of good or harm in the service menu.