You must use the correct spring...
You must use the correct spring height for the buttons to quarter-turn into. Attach the springs to the backside of the tabs with pop rivets.
A note about your choice of steel wheels: We found that some wheels that are otherwise for the same vehicle in every respect except possibly year of manufacture can have a different width of gap around a standard disc. With small hubcaps and trim rings, you'd never notice a variation. You may like a minimal amount of rim showing, or a larger gap to expose more of the color of your painted rim. It's your call, but you certainly want the amount of rim edge exposed to be the same on all four wheels. Try a Moon disc over all four of the wheels you want to use and center it, checking that all rim lips really are identical.
What's cool about the attachment method illustrated here, aside from avoiding the problem of screws, is that the discs are retained more securely (SCTA rules specify that if screws are used on a race car, you have to have six per wheel but only three Dzus buttons are required) and they are flush with the Moons. The look is clean. In our case we opted for using aluminum Dzus buttons, which can be sanded so they blend in even more subtly with the aluminum of the discs. The standard buttons are steel and can take a lot of abuse, but you have to be careful not to gouge the softer aluminum type. Buttons, springs, and plates are available from Moroso or your local speed shop. Living with Moon discs means you'll be carrying a removal tool in your glovebox. In a pinch, a quarter can be used (which lends another dimension to the term quarter-turn fastener), but avoiding slipping off the button and potentially scratching your discs demands a strong tool that perfectly fits the curved slot in the buttons. If this classic look appeals to you for your current or future project, or you're just tired of steeliness with the usual Merc hubcaps and trims rings, give the Moons-and-Dzus combo a try! It's hard to believe, but Mooneyes makes standard discs in diameters from 10 to 46 inches. You could put Moons on a fire truck or a semi.
There are several ways to...
There are several ways to install Dzus buttons. Most racers' toolboxes contain at least one stubby screwdriver with the end ground to match the curved slot in the buttons. When using aluminum buttons as we are, you need a no-slop fit to avoid marring the buttons or slipping onto the disc.
The typical commercial Dzus...
The typical commercial Dzus tool has a large round blade that can be used upright or laid down, which provides extra leverage when you have a tight-fitting button.
If there's any way to improve...
If there's any way to improve on the classic looks of traditional Moon discs, it would be a better way of securing them to your wheels. Using time-proven Dzus fasteners, your discs are secure, the look is flush and clean, and checking tire pressure without chipping your painted rims is easy.