The conversion is based on paragraph and character formats, not on elements, so you must use distinct format names to get distinct effects in the output. Specify a different format in your FrameMaker EDD for each element type that needs to be visually distinct in the output, rather than using Body with overrides for everything. In other words, use the EDD to create exactly the sort of formatting used in unstructured files.
If you are stuck with a one-format EDD, you can retain in the HTML most (but not all) of the overrides; however, you have to accomplish this with font tags and align attributes, which makes CSS pretty much useless for the resulting HTML.
> 12 Converting to HTML > 12.9 Converting structured documents to HTML