You can use below workarounds to restrict all users from modifying published analysis:
1) Folder Permissions:Save the dxp in one folder whose permissions would be browse+access for all users. That way even though Business Author users modify anything in dxp, they would not be able to overwrite the published dxp
2) Hide Viewing/Editing dropdown:You can alter css property for authoring dropdown in analysis. Below css style needs to be inserted in textarea on each tab
<style>
.sfx_author-dropdown_292 {
display:none;
}
</style>
Note this approach is not recommended as class names for attributes may change from version to version so after upgrade this functionality may stop working. Hence, this can be the last option if folder permissions approach do not work for your use case.