I don't want to align the color purity, just the tube itself mechanically because it sits at an angle. I doubt very much that NEC shipped it like that in 1987!
I've worked with scope CRTs, not so much TVs, I wanted to ask to be sure before I end up on the evening news.
Your chances of injury from an imploding 9" tube are about the same as flying to the moon on gossamer wings.
Tens of thousands of Techs changed hundreds of thousands of such (& very much larger) tubes over tens of years without incident.
Tubes are usually fitted with four mounting "ears".
The front panel usually has four threaded "studs" sticking out of it.
You fasten the tube in place with four hex nuts.
Just loosen these nuts enough that you can move the tube---the holes in the ears have enough "wiggle"room for you to get the tube level.
Hint:Find where there is a horizontal line across the display,& with a felt tip pen,draw a straight line across the tube face following the display line (Yes,Virginia,you
can draw lines on a tube face.).
It is a lot easier getting the tube level when the monitor is off,as you don't have to worry about putting your fingers on "hot" bits while you are concentrating on the screen.