Dynamic convergence was pretty common, later monitors had dynamic focus and dynamic landing correction also.
The one unexplored improvement was magnetic focus. It was abandoned in favor of electrostatic focus during WWII to save copper. But electrostatic focus has the inherent flaw that you can't have bright areas and dark areas both in perfect focus.
I doubt you could have used magnetic focus on a color CRT, but it was used on the very best CRT projectors. It is true that focus was the main limiting factor on resolution. Most high end CRTs could physically scan at higher resolutions than were really usable because things just got too blurry.
I wish the OP luck, but I doubt an individual could do better than Sony at driving a monitor CRT. Sony, and their competitors invested millions, and had whole teams of engineers plus decades of experience. The main improvement that could have been made was spending more time tweaking the various adjustments that affected convergence, focus, and geometry. Most CRTs could be made to look much better with an additional hour plus of alignment. I regularly did this to my own monitors, and TVs, and occasionally for customers. The difference could be quite dramatic.
Broadcast monitors at my old job at the TV always had that extra time spent on them, & the results were, as you say, "dramatic".
The monitors which were the hardest to get right were those used with the old AVA-Graphics suites, which
always used their RGB inputs, so PAL artifacts didn't make some errors less obvious.
They were big monitors, too--from memory, Sony BVM2000s.
The AVA operators were really strict------they would draw "squiggles" in the extreme corners of the display to check for any convergence errors.
If the monitor didn't didn't shape up, sometimes we could adjust them in the suite, with the operator putting up more "squiggles", but if that didn't work, it was "back to the bench".
Broadcast Picture Monitors were expensive & had operational lives of around 20 years, so they were pretty spectacular technological achievements.