It's diameter, mass and rpm that generate the angular momentum, i.e. gyroscopic effect. Most of the improvement you feel...and there will be substantially improved stability on pavement...will be from the tire. Seriously, you can't go more than about 2" taller on the tire, without clearance issues, with the suspension bottomed-out. Catch a front tire against the fender, while riding at any speed and you're heading over the bars...no joke. Stock tire size is spec'd at 56.5"; with stock suspension, ~61" is the limit before taller forks, shocks and a longer swingarm are needed.
Now, if we were to compare a CT70 to, say your newly-acquired 250, now there's more than enough diameter difference to make a big difference. Of course, there's also better suspension, longer wheelbase and one helluva lot more mass, all of which make a bike more stable. I can tell you, from firsthand experience, just adding a small passenger to a CT70 makes the machine far more stable than riding solo. That said, a certain amount of twitchiness (or "flickability", depending upon whom you ask) is part of the appeal of a small bike...bringing the high-speed aspects of riding down to much lower speeds and over much shorter distances. No matter what mods are done to bike the size of a Z50, or CT70, they'd never be as stable at, say, 70mph as your 250. It all boils down to basic physics.