My SA license is not available for me to look at the commands in detail.
My watersheds are generally not as flat as Florida. In the flat valley areas I do have, I find the need to "build" lots of walls to make the flows go in the right directions.
I think there is an option in the burn streams tool that tells Arc Hydro to bring the negative dem values up to zero. If you do have zero values and can't find that option, but still want to see if the negative numbers make a difference, you could use the CON() function to make anything negative 0.0 or slightly above. Then you could use that raster for the rest of the process. I also don't recall negative numbers being a problem. I'm in the SF Bay area and my elevations aren't all that high. I use the default burn values which I think the deepest is 1000 ft. and I know many of my projects have gone to the bay and I've never had a problem.
Since I have steeper terrain, my tendency is to minimize the width of the smooth and sharp rise values. The purpose of the smooth drop is to eliminate parallel stream right next to your main stream.
It might be a trial and error situation for you to figure out what values to use. When I do trial and error, I do a trial noting the parameters I used, get out of Arc Map, delete the Arc Hydro file geodatabase and raster folder, start up Arc Map again and reprocess using different smooth/sharp drop values. Seems to be a few extra steps, but makes things run with fewer hiccups due to overwrite conflicts etc. This is where model builder comes in handy.