@AaronShep . . . You could perhaps try installing and using the
HTML2Epub plugin. This plugin will import your html into Sigil and convert your html file direct to epub format -- which also certainly includes splitting the html file into separate sections denoted by the heading style that is used throughout. This plugin only works for html files that are specifically derived from
MS Word, LibreOffice Writer or Google Drive. Best read the release notes from the above link to find out whether this plugin would suit your needs or not.