I don't have a suggestion on a source for a press for a thinner patty, but I wholeheartedly agree with your need for one.
For me the thinner the better.
My smashburgers are always a consistent 56.7 grams uncooked weight. That is 2 oz., which for me turns out perfect to fit on a cheapo hamburger bun. (just like you get from your favorite greasy spoon burger joint.) That gives me exactly 8 burgers per pound of ground beef. (Has to be 80-20. 90-10 just won't do, not enough grease.
)
I sometimes like a thick burger, & 2 oz. of meat might sound pretty skimpy, but smash that baby flat and throw on a slice of American cheese, and the grease soaking into that bun will more than make up for the small amount of beef.
IMHO the perfect ratio for a great smashburger.