I had troubles with my lever drain stopper and got so fed up that I use a differnt method instead. I removed the linkage and stopper from the faceplate and just screwed the faceplate back on the tub. Then I bought a 5" flat disc at the grocery store called a drain stopper. It looks similar to this
but it's totally flat. Works great at holding the water in the tub and no more lever to worry about.
But if you're set on installing a new trip lever then I would just use your existing screws or new ones of the same size and install a stainless steel washer under them to hold the new faceplate in place.