Oak Tree leaves are the worst one to work with in FL
1. They are small to mulch.
2. Small enough to get into or between the St. Augustin grass roots (Hard to rake)
3. If you do mulch them first they have to be dry and 2nd since all the leaves are brown it doesn't look like you did anything after your done.
My opinion blow all the leaves in piles and load in a tarp or a large cloth. This will save you at least 1-2 hrs from bagging and then dumping.