I assume you're talking about a CRT & not an LCD, right?
Sometimes it can be tough to do what you're describing. But a lot depends on the quality of the monitor. I've used some cheapy monitors in the past that were utterly impossible to get the way you describe, but I've also used some better monitors that can get almost spot-on.
Curved face monitors (i.e., not flat screens) can be difficult, but true flat-screen CRTs are generally easier to get close to perfect, geometry-wise. Then there are pseudo flat screens -- screens that only have a flat glass over a curved tube. :roll: And you guessed it -- they can be difficult when it comes to achieving perfect geometry. You can also run into a phenomenon called "blooming," which is typically caused by a cheapy, weak power supply (in the monitor). Many inexpensive CRT monitors and televisions exhibit this problem, which manifests itself as 'wavy' or bent vertical lines. Manufacturers often use inadequate power supplies in CRT products to cut costs, and they feel they can get away with it 'cuz Average Joe is not a discerning viewer. If your CRT has blooming, no amount of adjustments are gonna fix it for good and the sides of your screen will look bent regardless. One thing you should try, however, if you haven't already, is adjusting the contrast. As I understand it, excessive contrast contributes to blooming & uneven geometry because it strains the power supply. Try dialing back the contrast a fair amount and then do your adjustments again & see if it helps. I can tell you that turning the contrast down on my CRT television cut the blooming by about half (if not more).
There is a test pattern for CRT computer monitors somewhere -- I had it bookmarked at one time, but seem to have deleted it. Maybe Google "CRT test pattern" or "computer monitor test pattern" or the like and see what comes up.
If you have anything but a high quality CRT, you might not be able to get the perfect geometry you're looking for. It depends on the brand, model, and the quality of the tube itself (& the monitor's power supply).
Gotta run and go tend to some Christmas goings-on, so good luck.