Two shops, Clever Cycles of Portland, OR and Dutch Bike Co. of Seattle got back to me recommending Workcycles, specifically the Secret Service. It is available down to 45 cm and is offered in a range of gearing that can handle Portland and Seattle, which means it can handle Austin.
My research tells me that WorkCycles is run by Henry Cutler, an American who lives in Amsterdam and runs both the brand and the shops. All by itself, sounds pretty cool! The Secret Service is a modernish take on the classic Dutch Omafiets made for smaller riders and longer distances than the frankly tank-like classics. The tubing and racks are a bit lighter, making it as sporty as a Dutch Omafiets gets. That being said, you can still move a kid, throw some groceries on the front rack, and leave it parked outside. So...that's basically the exact bike I was trying to come up with. I really wish I could test ride it,but maybe that's the bike to save up for next.