A lot of short scale basses are less than 19mm. A Squier Bronco for example, is 17mm.
You can find some aftermarket bridges. For example, this is an 18mm bridge by Song-Il http://www.sung-il.com/bbs/board.php?bo_table=b071_29
I'm sure there are others as well.
Best of luck with the hunt!
ESP Ltd B-1005, ESP Ltd Surveyor-4, ESP Ltd B-4Z (inbound) Squier VM Fretless P, Squire Affinity Jazz V Fretless (in work), Mesa Walkabout Scout