We have lacebark elms on my street which seed prolifically. I use pre-emergents such as preen and treflan and don't have a problem although I see them coming up in other yards. We do have heavy clay alkaline soil so I don't know how that translates to Florida sand.
Incidentally we had a major ice storm in February and the lacebark elms did not do well, although many are not named cultivars and are rather gangly. I don't suppose that's a big concern in Florida.
Ron
Cincinnati
member, ASCA, ISA, TCIA, ONLA, ISA OH-5177A