I use a carpenter's square across the top of the barrel, or receiver to check and adjust the staff on a tang sight. If the barrel is below receiver height, simply use a piece of flat material on top of the barrel to shim it up. You can adjust the staff on good quality tang sights so it sits vertical, or perpendicular to the bore.
As the aperture travels higher on the staff the angle to the front sight will also change slightly. But I've never worried about it, nor have I had any issues, even when adjusted well towards the top of the range for long distance shooting.
I personally don't shim bases, as i prefer to remove metal to adjust the staff to sit vertical side to side. But nothing wrong with shimming if that's what you prefer. I use the square along the side of the receiver also to check to see if the tang side leans either way. Just angle the square back towards the staff and use my dial caliper against the staff at base and top, to see how much out of perfect upright it is.

Try adjusting the staff by having a friend move the staff slightly fore and aft while in your shooting postion with head postioned as shooting. You’ll usually end up with the staff angling slightly forward towards the muzzle.

To keep my aperture hole "round" to my eye when elevated for 900-1200 yds I have my staff leaning forward at bit. Otherwise you would see an ellipse and fuzzy edge. I still struggle with my glasses to get a clean picture.
kw

I think the OP's question is how to set the rear tang sight so that it's perpendicular to the bubble on his front sight. 
If you can put your rifle in a padded vise, or in some kind of cradle to hold it, then confirm that your bubble is level on the front sight. Then take a little 6" level and put it along the staff of your tang sight and see if it is perpendicular (plumb). If not, you're going to have to put shim material underneath one side or the other of the base until the tang is perpendicular to your level in the front sight. You adjust the staff moving forward or backwards by a small screw in the base. You can loosen it which releases pressure on the spring which allows you to slide the staff for or aft a little bit until it's where you want it. I'm with those that lean it forward a little bit so that the holes in your aperture are round.
Sometimes you're front sight bubble is not in alignment with the side of the action. You might overcome that by loosening the screws that hold the bubble in the sight and sticking in some small piece of material (piece of styrofoam peanut) that will move the bubble a little bit up or down on one side that will help you get the rifle leveled according to the side of the receiver.

Shooting gongs is does not take less accuracy than shooting off a bench at 100 or 200yds. I'm getting a little tired of this constant comment every time the subject of accuracy comes up!
1 moa is 1" at 100 yds. So at 1000 yds., it's 10" and what happens to a bullet traveling through the atmosphere at 100 yds. or 200 yds. has far less effect on the bullet, than what happens to the same bullet traveling to a 10 moa target at 1000 yds. with the bullet exiting over the speed of sound, dropping back through it, and at an arc that's 60 ft. above the ground and all those wind flags people shooting 200 yds. use.
If some person with zero knowledge of shooting past 200 yds. from the bench thinks that hitting a target at 1000 yds. takes less accuracy or skill then they need to test themselves by trying it, and then tell everybody how easy it is, or how little sight adjustments mean at 1000 yds.

On the other hand, there is the Buffington sight with its built in lean to compensate for rifling drift.

For 100 yard rest shooting that 1 inch has to be cut in half to be able to get 10 consecutive shots into a 3/4 inch 25 ring. Same holds true for 200 yards all though it actually needs to be less to leave room for the conditions.
Are you putting 10 consecutive shots inside of a 10 inch ring at 1000 yards and if so you might actually be right.